We want to form a committee consisting of 3 men and 3 women, from a group of 8 women and 6 men. How many possible ways are there to form the committee if:

Question

Mathematics

Kenley Webster

17 September, 14:05

We want to form a committee consisting of 3 men and 3 women, from a group of 8 women and 6 men. How many possible ways are there to form the committee if:

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Answers (1)

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Caden Mercado · Answer 1

1120 possible ways

Step-by-step explanation:

In order to find the answer we need to be sure what equation we need to use.

From the given example, let's consider initially only men. Because you have a total of 8 men and we need to chose only 3 men, let's suppose that the 3 chosen men are A, B, and C.

Because A, B, C is the same as choosing C, B, A, which means it doesn't matter the order of the chosen men, we need to use a 'combination equation'.

Because we have two groups (women and men) then we have:

Possible ways = 8C3 * 6C3 (which are the combinations for women and men respectively). Remember that:

nCk=n! / ((n-k) !*k!) so:

Possible ways = 8! / ((8-3) !*3!) * 6! / ((6-3) !*3!) = 56 * 20 = 1120.

In conclusion, there are 1120 possible ways.