Six married couples decide to form a committe | vedclass

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

Question

(B) We have $6$ married couples,which means a total of $12$ people.To form a committee of $6$ persons such that no couple is included,we must first se

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(B) We have $6$ married couples,which means a total of $12$ people.To form a committee of $6$ persons such that no couple is included,we must first select $6$ couples out of the $6$ available couples. This can be done in $\binom{6}{6} = 1$ way.From each of the $6$ selected couples,we must choose exactly one person to be on the committee. Since each couple has $2$ members,there are $2$ choices for each of the $6$ positions.Therefore,the total number of ways is $\binom{6}{6} 	imes 2^6 = 1 	imes 64 = 64$.

Six married couples decide to form a committee of $6$ persons. The total number of ways to form the committee such that it contains no couples is equal to:

Similar Questions

How many $3$-digit numbers can be formed by using the digits $1, 3, 6,$ and $8$,when the digits may be repeated any number of times?

If $^{2n}C_3 : ^nC_2 = 44:3$,then for which of the following values of $r$,the value of $^nC_r$ will be $15$?

$A$ question paper has $2$ parts,part $A$ and part $B$,each containing $10$ questions. If a student has to choose $8$ questions from part $A$ and $5$ questions from part $B$,in how many ways can the student choose the questions?

There are $15$ buses running between Delhi and Mumbai. In how many ways can a man go to Mumbai and return by a different bus?

In how many different ways can the letters of the word '$AUCTION$' be arranged in such a way that the vowels always come together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module