SOLUTION: The neighborhood association with sixteen members also needs to select a committee of four to oversee fundraising. How many possible committees are there?

Question 167634: The neighborhood association with sixteen members also needs to select a committee of four to oversee fundraising. How many possible committees are there?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Since order does not matter (ie no member on the committee is more important than the other), we must use the combination formula:

Start with the combination formula

Plug in and

Subtract to get 12

Expand 16!

Expand 12!

Cancel

Simplify

Expand 4!

Multiply 16*15*14*13 to get 43,680

Multiply 4*3*2*1 to get 24

Now divide

So 16 choose 4 (where order doesn't matter) yields 1,820 unique combinations

So there are 1,820 ways to choose a committee of 4 members given a pool of 16 people.
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