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A class has 17 ​students, of which 3 are seniors. How many committees of size 3...

A class has 17 ​students, of which 3 are seniors. How many committees of size 3 can be selected if at least one member of each committee must be a​ senior?

The number of committees is?

Math   Statistics-And-Probability   
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Answer #1

Answer: 316

Explanation:

Since there are 3 seniors so there are 14 non-seniors.

So, number of committees with at least one senior member is given as:

All Possibilities - Possibilities of Number of committees with No Senior

Now, All Possibilites =

  

And, Possibilities of Number of committees with No Senior

So, the number of committees with at least one senior member = 680 - 364 = 316

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