SOLUTION: In how many ways can we pick a three-person committee from 7 people?

Question 1042610: In how many ways can we pick a three-person committee from 7 people?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
There are 7 ways to fill slot A
There are 6 ways to fill slot B (since we can't have any one person serve more than two posts)
There are 5 ways to fill slot C

There are 7*6*5 = 42*5 = 210 different ways to fill the three slots (from a pool of 7). This is where order matters.

Since we're talking about a committee, this means order doesn't matter. Any one member doesn't outrank the other.

Since order doesn't matter, we have to divide by 6. Why 6? Because this is the number of ways to arrange 3 people. 3! = 3*2*1 = 6

210/6 = 35

The final answer is 35. There are 35 ways to pick three people from a pool of seven where order does NOT matter.
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