Our school’s girls volleyball team has 14 players, including a set of
3 triplets: Alicia, Amanda, and Anna. In how many ways can we
choose 6 starters if at most one of the triplets is in the starting lineup? There can't be 2 or more triplets and there can be none.

Answers

Answer 1

Answer:

[tex]1,\!848[/tex].

Step-by-step explanation:

There are two disjoint sets of ways to choose a lineup as required:

Include none of Alicia, Amanda, or Anna, orInclude exactly one of Alicia, Amanda, and Anna.

Assume that none of Alicia, Amanda, or Anna is to be selected. This lineup of [tex]6[/tex] would then need to be selected from a set of [tex]14 - 3 = 11[/tex] players (which excludes Alicia, Amanda, and Anna.)

The number of ways of selecting (without order) [tex]6[/tex] items out of a set of [tex]11[/tex] (distinct) items is equal to the combination:

[tex]\begin{aligned}\begin{pmatrix}11 \\ 6\end{pmatrix} &= \frac{11!}{(6!)\, (11 - 6)!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].

Assume that Alicia is selected, but neither Amanda nor Anna is selected. The other [tex]6 - 1 = 5[/tex] players in this lineup would then need to be selected from a set of [tex]14 - 1 - 2 = 11[/tex] players. (This set of [tex]11[/tex] excludes Alicia, Amanda, and Anna.)

The number of ways to select [tex]5[/tex] items from a set of [tex]11[/tex] items is:

[tex]\begin{aligned}\begin{pmatrix}11 \\ 5\end{pmatrix} &= \frac{11!}{(5!)\, (11 - 5)!} \\ &= \frac{11!}{5! \times 6!} \\ &= \frac{11!}{6! \times 5!}\end{aligned}[/tex].

Similarly, there would be another set of [tex](11!) / (6! \times 5!)[/tex] distinct ways to select the lineup if Amanda is selected, but neither Alicia nor Anna is.

Likewise, the number of ways to select the lineup with Anna but neither Amanda nor Alicia would also be [tex](11!) / (6! \times 5!)[/tex].

These sets of configurations for the lineup are pairwise disjoint from one another. Thus, the total number of ways to select this lineup would be:

[tex]\begin{aligned}& \begin{pmatrix}11 \\ 6 \end{pmatrix} + 3 \times \begin{pmatrix}11 \\ 5 \end{pmatrix} \\ =\; & \frac{11!}{6! \times 5!} + 3 \times \frac{11!}{6! \times 5!} \\ =\; & \frac{4 \times 11!}{6! \times 5!} \\ =\; & \frac{4 \times 11 \times 10 \times 9 \times 8 \times 7}{5 \times 4 \times 3 \times 2} \\ =\; & \frac{11 \times 10 \times 9 \times 8 \times 7}{5 \times 3 \times 2} \\ =\; & 1,\!848\end{aligned}[/tex].


Related Questions

train covers 20 km in one hour then how much distance will it cover in 1 min?

Answers

[tex]\sf\large\underline{Given:-}[/tex]

Speed of the train = 20km / 1hr.

[tex]\rightarrow[/tex] 1 hour = 60 minutes.

So, speed of the train = 20km/60min.

[tex]\sf\large\underline{To\: Find:-}[/tex]

[tex]\rightarrow[/tex]Distance covered by train in 1min.

[tex]\sf\large\underline{Solution:-}[/tex]

Let the distance covered by train in 1 min be [tex]\sf{x}[/tex] m.

So, if train covers 20 km in 60min then it covers [tex]\sf{x}[/tex] m in 1 min.

It can be written as,

[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}}[/tex] [tex]\sf{=\frac{x}{1}}[/tex](by cross multiplication)

[tex]\rightarrow[/tex][tex]\sf{20\: = \: 60x}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}= x}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{\frac{1}{3}= x}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{0.33= x}[/tex](approx)

Therefore, distance covered by train in 1 min= 0.33km (approx).

_______________________________

Hope it helps you:)

Which of the following describes the solution to a system of linear inequalities?
A. The soultion is the region where both shaded parts overlap.
B. The solution is everything on the shaded graph.

Answers

Answer:

A. The solution is the region where both shaded parts overlap.

Step-by-step explanation:

The solution to a system of linear inequalities is the intersection region of the solution of both inequalities. Or you could also say that it's the region where the graphs of the inequalities in the system overlap.

The shaded area represents the solution and where the two inequalities overlap.

The mean weight of three people in a lift was 62kg. If two of them weighed 55kg each, how much did the third person weigh?

Answers

Answer:

72 kg

Step-by-step explanation:

let weight of third person=x

62-55=x-62

7=x-65

x=7+65=72 kg

Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 'of an inch, it is 4 3/4 'inches.
a) What is the largest the actual height the plant could be?
b) What is the smallest the actual height the plant could be?
c) How large could the percent error in Jada’s measurement be?

Answers

Answer:

See below.

Step-by-step explanation:

a) 4 7/8 inches

b) 4 5/8 inches

c) 12.5%

A point located at (1, 8) is reflected over the x-axis. What are the coordinates of the image?

(-1, 8)
(8, 1)
(-1, -8)
(1, -8)

Answers

Answer:

(1, -8)

Step-by-step explanation:

In this case, we are reflecting. Since we are reflecting over the x axis, the only thing that will change will be the y.

----------------------------------------------------------------------------------------------------------

The x is staying the same because it is not moving. The y, however, is changing sides.

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Since the y is positive in its original spot, when you reflect over the x axis, you will have a negative y value, which is why it is a -8.

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I hope this helps!

-No one

Can someone please help me with this thank you

Answers

Answer:

The skeletal system has many functions. Besides giving us our human shape and features, it:

Allows movement: Your skeleton supports your body weight to help you stand and move. Joints, connective tissue and muscles work together to make your body parts mobile.

Produces blood cells: Bones contain bone marrow. Red and white blood cells are produced in the bone marrow.

Protects and supports organs: Your skull shields your brain, your ribs protect your heart and lungs, and your backbone protects your spine.

Stores minerals: Bones hold your body’s supply of minerals like calcium and vitamin D.

100.2and 19.400 which is greater​

Answers

Answer:

19.400

Step-by-step explanation:

19.400 equals out to 42769.67886386625

Is a 779 a good MI score

Answers

Answer:

yes

explanation:

Your score falls within the range of scores, from 740 to 799, that is considered Very Good. A 779 FICO Score is above the average credit score. Consumers in this range may qualify for better interest rates from lenders.

Yes you are smart alway remember that

B. To make salad dressing for the fruit salad, Mrs. Santos uses 2/4 cup oil, 1 cup orange juice, and 3/4 cup honey. How many cups of salad dressing does this make? Explain how you found your answer.

Answers

Answer:

[tex]\sf 2 \frac14 \ cups[/tex]

Step-by-step explanation:

Add the amounts together:

[tex]\sf \implies \dfrac24+1+\dfrac34[/tex]

Convert the whole number 1 into a fraction with denominator 4:

[tex]\sf \implies \dfrac24+\dfrac44+\dfrac34[/tex]

As all the denominators are the same, we can simply add the numerators:

[tex]\sf \implies \dfrac{2+4+3}4[/tex]

[tex]\sf \implies \dfrac94[/tex]

Finally, convert the improper fraction into a mixed number:

[tex]\sf \implies 2 \frac14 \ cups[/tex]

Add all

[tex]\\ \rm\rightarrowtail \dfrac{2}{4}+\dfrac{3}{4}+\dfrac{4}{4}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{2+3+4}{4}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{9}{4}[/tex]

[tex]\\ \rm\rightarrowtail 2\dfrac{1}{4}cups[/tex]

The measure of an angle is 107.4 what is the measure of its supplemental angle ?

Answers

Answer:

72.6

Step-by-step explanation:

180-107.4 = 72.6

Solve for X -3x + -6 = 21

Answers

Answer:

x= -13.5

Step-by-step explanation:

X-3x+(-6)=21

-2x-6=21

-2x=27

2x=-27

x=-13.5

Help? Anything can help I’m in a rush

Answers

Answer: A vertical line from (-5 , 4 ) to (5 , 4)

Step-by-step explanation: The y axis is the vertical  one. Go up 4 and draw a line connecting all the points with 4 in the coordinates.

Hope that helps :)

Answer:

Step-by-step explanation:

go up 4 lines on the y-axis then draw a straight line from left to right on y=4

I don't know if you can see the picture, but I drew a line on the picture you provided...

Please 5 stars if correct!!!

I hope this helps

what is the answer
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Answers

Answer:

-8.9° C

Step-by-step explanation:

Question:

Doing a scientific experiment the temperature of a container decreased by 35.7° C at a constant rate over 8 1/2 hours.

What value represents the change in the temperature of the container each hour?

Answer:

-8.9° C

A flag is created by sewing together

Answers

Answer:

yes, a flag is created by sewing it together

camilo uses 32 ounces of filling to make empanadas. he puts 8 empanadas on each of 3 trays. Write a fraction to show how many ounces of filling camilo uses in each empanada. Please reply quickly!

Answers

Answer:

32/4

Step-by-step explanation:

 

What is the area of the figure below?
A. 16
B. 45
C. 51
D. None of these

Answers

Answer:

C. 51

Step-by-step explanation:

For Square:

Length x Height

7 x 6 = 42

For Triangle:

Base x Height x 1/2

(6x3)1/2 = 9

42 + 9 = 51

The recent price of a car is Rs.10,00,000. If its price reduces by 10% yearly, after how many years it's price will be Rs. 7,29,000? Find it.​

Answers

Answer:

hope it helps

also do write the givens

Find the actual area of the triangle below.
Can someone pls help?

Answers

Answer:

200 meters2

Step-by-step explanation:

4 * 5 = 20

20 * 20 ÷ 2 = 200

How many terms are in the expression? 9a + 6b + 3c + 1 A) 1 B) 2 C) 3 D) 4

Answers

Answer:

D.) there is 9a and 6b ,3c and 1 thats four different terms

Step-by-step explanation:

Have a nice day! :D

the length of a rectagle is twice its width. if the perimeter of the rectangle is 36in, find its length and width

Answers

Answer:

Perimeter=36in

Length of one side=12

Length of the other side=12

Width of one side=6

Width of the other side=6

Step-by-step explanation:

6*2=12, so if the length is 12 half would be six. All of them added up is 36

Answer:

Length = 12inWidth = 6in

Step-by-step explanation:

[tex]perimeter \: of \: a \: rectangle = 2(2x) + 2(x) \\ 36in = 4x + 2x = 6x \\ \frac{36in}{6} = \frac{6x}{6} \\ x = 6in \\ 2x = 2 \times 6in = 12in[/tex]

Mark me brainliest!


7. The area of the parallelogram is 450 m2. What is
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A. 25 m
B. 36 m
C. 50 m
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Answers

The answer is 36 sq. ft. Find the area of the following parallelograms. Example 3. Base = 7 meters, Height = 3.5 meters. First, write

h = height of the parallelogram. a = side of the parallelogram (AD) x = any angle between the sides of the parallelogram (∠DAB or ∠ADC) d1 = diagonal of the parallelogram (p)
...
Area = ½ × d1 × d2 sin (y)

Convert to vertex form: f(x) = x2 + 16x + 64


Answers

Answer:

Step-by-step explanation:

hello :

note : the vertex form is :

ax²+bx+c = a(x+(b)/(2a))²-  delta/4a²   and   delta = b²- 4ac

in this exercice you have : a =1    b = 16   and  c=64

continu ..........

Cassie has 10 1/2 feet of string to make 15 beaded bracelets. She needs 9 inches of string for each bracelet. Does she have enough string to make all the bracelets? Explain. (1 foot = 12 inches) ​

Answers

Answer:

unfortunately one person will be without a bracelet

If two chords are the same distance from the center of a circle, then they are ______.

Answers

Answer:

1 is the answer to have the distance same

1. quadrilateral with 4 right angles

Answers

Answer:

Square

Step-by-step explanation:

Find the area of the figure

Answers

Answer:

88 cm²

Step-by-step explanation:

88 cm² is your answer

Tan^2xsin^2x=tan^2x-sin^2x
Prove identity

Answers

Answer:

See below for proof

Step-by-step explanation:

[tex]\tan^2x\sin^2x\\\\(\sec^2x-1)(\sin^2x)\\\\(\frac{1}{\cos^2x}-\frac{\sin^2x}{\sin^2x})(\sin^2x)\\\\(\frac{\sin^2x-\sin^2x\cos^2x}{\sin^2x\cos^2x})(\sin^2x)\\\\\frac{\sin^2x-\sin^2x\cos^2x}{\cos^2x}\\\\\frac{\sin^2x}{\cos^2x}-\sin^2x\\\\\tan^2x-\sin^2x[/tex]

Hence, the identity is proven

Brand 1 Brand 2 Brand 3 Store 1 Store 2 Store 3 Laptop Comparison Chart Criteria for laptop search: Laptop specifications: • At least 3GB of memory • At least 250 GB hard drive • At least 14” Screen • Weigh at most 7 pounds • At least a 1 year manufacturer warranty • Built-in wireless router • Must be new, not used of refurbished Spending Limit: $800 • Includes laptop, sales tax, and shipping • For the purpose of this project, use 7.5% sales tax

Answers

The total amount that will be paid for the products with a sales tax of 7.5% will be $1290.

How to compute the amount from the sales tax?

Your information isn't complete as the table denoting the appropriate values aren't given.

Let's assume that the price of a product A is given as $800 ane product B is $400. If the sales tax is 7.5%, the total amount that will be paid will be:

= ($800 + $400) + (7.5% × $1200)

= $1200 + $90

= $1290

Learn more about sales tax on:

https://brainly.com/question/9437038

If 12Kg of chicken feed cost 20 how much would 5kg cost?
and what is the unit rate? ( price per 1 kg)

Answers

Step-by-step explanation:

if you 12kg cost 20 what about 5kg that will be 5kg×20÷12kg= 8.33 when you round of to the nearest hundredth this is the price of 5kg

sorry but i dont think i know how to answer the other question i have done what i only know thankyou

What is the average rate of change of the function y = 3 cos x on the interval [π/2, π]?

Answers

Answer:

¹

Step-by-step explanation:

Average Rate of Change is

ts

[tex] \frac{f(b) - f(a)}{b - a} [/tex]

Here b is pi, a is pi/2,

[tex] \cos(\pi) = - 1[/tex]

[tex] \cos( \frac{\pi}{2} ) = 0[/tex]

So we have

[tex] \frac{ - 1 - 0}{ \frac{\pi}{2} } = \frac{ - 1}{ \frac{\pi}{2} } [/tex]

Answer:

-2/pi

Step-by-step explanation:

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