It is required to seat 5 men and 4 women in a | vedclass

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

Question

(A) Total number of people $= 5$ men $+ 4$ women $= 9$ people.In a row of $9$ positions,the even places are the $2^{nd}, 4^{th}, 6^{th},$ and $8^{th}$

Vedclass · Accepted Answer

$2880$

Vedclass · Answer

(A) Total number of people $= 5$ men $+ 4$ women $= 9$ people.In a row of $9$ positions,the even places are the $2^{nd}, 4^{th}, 6^{th},$ and $8^{th}$ positions.There are $4$ even places available,and there are $4$ women to occupy these positions.Therefore,the number of ways to arrange the women in the even places is $P(4, 4) = 4! = 24$.There are $5$ remaining odd positions $(1^{st}, 3^{rd}, 5^{th}, 7^{th}, 9^{th})$ and $5$ men to occupy these positions.Therefore,the number of ways to arrange the men in the remaining positions is $P(5, 5) = 5! = 120$.By the fundamental principle of counting,the total number of arrangements is $P(4, 4) 	imes P(5, 5) = 4! 	imes 5!$.Total arrangements $= 24 	imes 120 = 2880$.

It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

Similar Questions

Find the number of ways in which two Americans,two British,one Chinese,one Dutch,and one Egyptian can sit at a round table so that persons of the same nationality are separated.

In how many different ways can the letters of the word $TABLE$ be arranged?

How many five-digit numbers can be formed using the digits $2, 0, 4, 3, 8$ if repetition of digits is not allowed?

How many numbers can be formed with the digits $1, 2, 3, 4, 3, 2, 1$ so that odd digits always occupy the odd places?

Out of $18$ points in a plane,no three are in the same straight line except five points which are collinear. The number of $(i)$ straight lines,$(ii)$ triangles which can be formed by joining them is

Vedclass Test Series

Exam Paper Generator

Online Exam Module