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(C) Total number of ways to choose a committee of $3$ people from $38$ is $\binom{38}{3}$.If you are on the committee,then you have already been selec

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$\frac{\binom{37}{2}}{\binom{38}{3}}$

Vedclass · Answer

(C) Total number of ways to choose a committee of $3$ people from $38$ is $\binom{38}{3}$.If you are on the committee,then you have already been selected,and we need to choose the remaining $2$ members from the remaining $37$ people.The number of ways to choose the remaining $2$ members is $\binom{37}{2}$.Therefore,the probability that you will be on the committee is the ratio of the number of favorable outcomes to the total number of outcomes:$P = \frac{\binom{37}{2}}{\binom{38}{3}}$.

If a committee of $3$ is to be chosen from a group of $38$ people of which you are a member,what is the probability that you will be on the committee?

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