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

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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 $(B_1, G_1)$ 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:

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