JEE MAIN - Mathematics (2017 - 9th April Morning Slot - No. 3)
The number of ways in which 5 boys and 3 girls can be seated on a round table if a
particular boy B1 and a particular girl G1 never sit adjacent to each other, is :
5 $$ \times $$ 6!
6 $$ \times $$ 6!
7!
5 $$ \times $$ 7!
Explanation
Number of ways = Total - when B1 and G1 sit together
Total ways to seat 8 people on round table = (8 - 1)! = 7!
When B1 and G1 sit together then assume B1 and G1 are one people, so total 7 people are there and among B1 and G1 they can sit 2! ways.
So total no of ways when B1 and G1 sit together
= (7 - 1)! $$ \times $$ 2! = 6! $$ \times $$ 2!
Number of ways = 7! - 6! $$ \times $$ 2! = 6!$$ \times $$(7 - 2) = 5 $$ \times $$ 6!
Total ways to seat 8 people on round table = (8 - 1)! = 7!
When B1 and G1 sit together then assume B1 and G1 are one people, so total 7 people are there and among B1 and G1 they can sit 2! ways.
So total no of ways when B1 and G1 sit together
= (7 - 1)! $$ \times $$ 2! = 6! $$ \times $$ 2!
Number of ways = 7! - 6! $$ \times $$ 2! = 6!$$ \times $$(7 - 2) = 5 $$ \times $$ 6!
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