The number of ways in which 5 boys and 3 girl | vedclass

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

Question

(A) Total number of people = $5 + 3 = 8$. Total ways to seat $8$ people on a round table = $(8 - 1)! = 7!$. Now,consider the case where $B_1$ and $G_1

Vedclass · Accepted Answer

$5 	imes 6!$

Vedclass · Answer

(A) Total number of people = $5 + 3 = 8$. Total ways to seat $8$ people on a round table = $(8 - 1)! = 7!$. Now,consider the case where $B_1$ and $G_1$ sit together. Treat $(B_1G_1)$ as one unit. Now we have $7$ units to arrange in a circle,which can be done in $(7 - 1)! = 6!$ ways. Within the unit,$B_1$ and $G_1$ can be arranged in $2! = 2$ ways. So,the number of ways they sit together = $2 	imes 6!$. The number of ways they never sit adjacent = Total ways - Ways they sit together. $= 7! - (2 	imes 6!) = (7 	imes 6!) - (2 	imes 6!) = (7 - 2) 	imes 6! = 5 	imes 6!$.

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,is

Similar Questions

How many odd numbers less than $1000$ can be formed using the digits $0, 2, 5, 7$? (repetition of digits is allowed).

If $a_n = \sum_{r = 0}^n \frac{1}{^nC_r}$,then $\sum_{r = 0}^n \frac{r}{^nC_r}$ equals

The value of $^n{P_r}$ is equal to

All possible two-factor products are formed from the numbers $1, 2, 3, 4, \dots, 200$. The number of products out of the total obtained which are multiples of $5$ is:

How many permutations can be made by using all the letters of the word $MATHEMAGICA$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module