There are 6 men and 8 women in a club in whic | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The club consists of $6$ men and $8$ women.We need to form a committee of $5$ people.If no man is selected,all $5$ members of the committee must b

Vedclass · Accepted Answer

$56$

Vedclass · Answer

(C) The club consists of $6$ men and $8$ women.We need to form a committee of $5$ people.If no man is selected,all $5$ members of the committee must be chosen from the $8$ women.The number of ways to select $5$ women out of $8$ is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Substituting the values,we get ${}^{8}C_{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5!3!}$.This simplifies to $\frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 8 	imes 7 = 56$.Thus,there are $56$ ways to form the committee.

There are $6$ men and $8$ women in a club in which a committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if no man is selected?

Similar Questions

There are $5$ letters and $5$ directed envelopes. Find the number of ways in which the letters can be put into the envelopes so that all are not put in directed envelopes?

The number of arrangements of all digits of $12345$ such that at least $3$ digits will not come in their original positions is

The number of ways in which $10$ persons can go in two boats so that there may be $5$ on each boat,supposing that two particular persons will not go in the same boat is:

$A$ committee of $4$ persons is to be formed from $2$ ladies,$2$ old men,and $4$ young men such that it includes at least $1$ lady,at least $1$ old man,and at most $2$ young men. The total number of ways in which this committee can be formed is:

In how many ways can $10$ people line up at a ticket window of a cinema hall?

Vedclass Test Series

Exam Paper Generator

Online Exam Module