Math CentralQuandaries & Queries


Question from danielle, a student:

I was wondering: What is the probability that both Barb and Bob are both on the same committee of 4 which is chosen fom their class of 10 people?

Is it 2/5? Thanks a bunch!


I: How many committees of 4 people can be formed from 10 people? This is the number of ways of choosing 4 things from 10 things.
II: How many of these committees have Barb and Bob on them? You can form such a committee by first placing Barb and Bob on the committee and then choosing 2 people from the remaining 8. Thus the answer to II is the number of ways of choosing 2 things from 8 things.

The probability that the committee you form has Barb and Bob on it is then the answer to II divided by the answer to I.

I hope this helps,

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