In how many ways can a group of 5 men and 2 w | vedclass

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Question

(A) The number of ways to select $5$ men from $7$ men is given by ${}^{7}C_{5}$.Using the property ${}^{n}C_{r} = {}^{n}C_{n-r}$,we have ${}^{7}C_{5}

Vedclass · Accepted Answer

$63$

Vedclass · Answer

(A) The number of ways to select $5$ men from $7$ men is given by ${}^{7}C_{5}$.Using the property ${}^{n}C_{r} = {}^{n}C_{n-r}$,we have ${}^{7}C_{5} = {}^{7}C_{2} = \frac{7 	imes 6}{2 	imes 1} = 21$.The number of ways to select $2$ women from $3$ women is given by ${}^{3}C_{2}$.Using the property ${}^{n}C_{r} = {}^{n}C_{n-r}$,we have ${}^{3}C_{2} = {}^{3}C_{1} = 3$.Therefore,the total number of ways to form the group is ${}^{7}C_{5} 	imes {}^{3}C_{2} = 21 	imes 3 = 63$ ways.

In how many ways can a group of $5$ men and $2$ women be made out of a total of $7$ men and $3$ women?

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