# Inaclubthereare1womenand 7 men. A committee of 5 women and 3 men is to be chosen. How many different ways are there to select the committee?

In a club there are 11 women and 7 men. A committee of 5 women and 3 men is to be chosen. How many different ways are there to select the committee?

### 7 Answers

- Anonymous8 months ago
1 women?

I don't think so.

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- KrishnamurthyLv 78 months ago
In a club there are 11 women and 7 men.

A committee of 5 women and 3 men is to be chosen.

The number of different ways to select the committee:

11C3 × 7C3 = 5,775

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- PuzzlingLv 78 months ago
Updated question: "In a club there are 11 women and 7 men. A committee of 5 women and 3 men is to be chosen. How many different ways are there to select the committee?"

From the 11 women, choose 5

C(11,5) = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1)

= 462

From the 7 men, choose 3

C(7,3) = (7 * 6 * 5) / (3 * 2 * 1)

= 35

Multiply these together to get the total number of possible committees.

462 * 35

= 16,170 ways

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- Geeganage WLv 58 months ago
Different ways of selection = 11C5 + 7C3 = 11!/(6!)(5!) + 7!/(4!)(3!) = 497.

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- ?Lv 78 months ago
There are 0 ways to get a committee with 5 women in it from a sample pool with 1 woman.

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- 8 months ago
Zero! you can't have a committee with five women if there's only one woman in the club

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