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Mekhanik [1.2K]
3 years ago
13

Suppose that a department contains 9 men and 15 women. How many different committees of 6 members are possible if the committee

must have strictly more women than men?
Mathematics
1 answer:
Drupady [299]3 years ago
8 0

Answer:  The required number of different possible committees is 81172.

Step-by-step explanation:    Given that a department contains 9 men and 15 women.

We are to find the number of different committees of 6 members that are possible if the committee must have strictly more women than men.

Since we need committees of 6 members, so the possible combinations are

(4 women, 2 men), (5 women, 1 men) and (6 women).

Therefore, the number of different committees of 6 members is given by

n\\\\\\=^{15}C_4\times ^9C_2+^{15}C_5\times ^9C_1+^{15}C_6\\\\\\=\dfrac{15!}{4!(15-4)!}\times \dfrac{9!}{2!(9-2)!}+\dfrac{15!}{5!(15-5)!}\times \dfrac{9!}{1!(9-1)!}+\dfrac{15!}{6!(15-6)!}\\\\\\\\=\dfrac{15\times14\times13\times12\times11!}{4\times3\times2\times1\times11!}\times\dfrac{9\times8\times7!}{2\times1\times7!}+\dfrac{15\times14\times13\times12\times11\times10!}{5\times4\times3\times2\times1\times10!}\times\dfrac{9\times8!}{1\times8!}+\dfrac{15\times14\times13\times12\times11\times10\times9!}{6\times5\times4\times3\times2\times1\times9!}\\\\\\=1365\times36+3003\times9+5005\\\\=49140+27027+5005\\\\=81172.

Thus, the required number of different possible committees of 6 members is 81172.

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Answer:

C

Step-by-step explanation:

The x- intercept is where the line crosses the x- axis. At this point on the x- axis the y- coordinate is zero.

To find the x- intercept let y = 0 in the equation and solve for x, that is

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5x = 2 ( divide both sides by 5 )

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G(a)=a-5 <br> h(a)=2a-4 <br> find g(h(1))
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Calculate h(1):

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In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect and . Then, i
ss7ja [257]

The measure of ∠ABP and ∠ABC are 32° and 64° respectively.

<h3>what is a bisector of an angle?</h3>

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5 0
4 years ago
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