Question: Committee of 4 people

Comment on Committee of 4 people

In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women..
Plz explain me this.
greenlight-admin's picture

Take the task of creating a committee and break it into stages.

STAGE 1: Select the 5 men for the committee
Since the order in which we select the men does not matter, we can use combinations.
We can select 5 men from 8 men in 8C5 ways (56 ways)
So, we can complete stage 1 in 56 ways

STAGE 2: Select the 6 women for the committee
We can select 6 women from 10 women in 10C6 ways (210 ways)
So, we can complete stage 2 in 210 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a committee) in (56)(210) ways.

Answer: 11,760 possible committees

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