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

The number of words that do not start and end with vowels,formed using all the letters of the word $UNIVERSITY$ such that all vowels are in alphabetical order,is

The number of four-digit natural numbers which contain exactly two distinct digits is:

Given six line segments of lengths $2, 3, 4, 5, 6, 7$ units,the number of triangles that can be formed by these lines is

How many words can be made from the letters of the word $BHARAT$ in which $B$ and $H$ never come together?

How many arrangements can be made of the letters of the word '$ARRANGEMENT$'?

Vedclass Test Series

Exam Paper Generator

Online Exam Module