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Three men (out of 7) and 3 women (out of 6) will be chosen to serve on a committee. In how many ways can the committee be formed?
Take the task of seating the 6 people and break it into stages.
Stage 1: Select 3 men to be on the committee Since the order in which we select the men does not matter, we can use combinations. We can select 3 men from 7 men in 7C3 ways (35 ways) So, we can complete stage 1 in 35 ways
Stage 2: Select 3 women to be on the committee Since the order in which we select the women does not matter, we can use combinations. We can select 3 women from 6 women in 6C3 ways (20 ways) So, we can complete stage 2 in 20 ways
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 6-person committee) in (35)(20) ways (= 700 ways)