In how many ways can a committee,consisting o | vedclass

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

Question

(C) To form the committee,we need to select $5$ men from $8$ and $6$ women from $10$.The number of ways to select $5$ men from $8$ is given by the com

Vedclass · Accepted Answer

$11760$

Vedclass · Answer

(C) To form the committee,we need to select $5$ men from $8$ and $6$ women from $10$.The number of ways to select $5$ men from $8$ is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.${}^{8}C_{5} = {}^{8}C_{8-5} = {}^{8}C_{3} = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$.The number of ways to select $6$ women from $10$ is ${}^{10}C_{6} = {}^{10}C_{10-6} = {}^{10}C_{4}$.${}^{10}C_{4} = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1} = 10 	imes 3 	imes 7 = 210$.By the fundamental principle of counting,the total number of ways to form the committee is ${}^{8}C_{5} 	imes {}^{10}C_{6} = 56 	imes 210 = 11760$.

In how many ways can a committee,consisting of $5$ men and $6$ women,be formed from $8$ men and $10$ women?

Similar Questions

If $^{43}C_{r-6} = ^{43}C_{3r+1}$,then the value of $r$ is

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is: (in $(7!)$)

$8$-digit numbers are formed using the digits $1, 1, 2, 2, 2, 3, 4, 4$. The number of such numbers in which the odd digits do not occupy odd places is:

How many $4$-digit numbers are there with distinct digits?

In how many ways can $15$ different books be divided equally among $3$ sets or groups?

Vedclass Test Series

Exam Paper Generator

Online Exam Module