Question
Question: In how many ways 6 boys and 5 girls can be seated in a row such that two girls are never together?...
In how many ways 6 boys and 5 girls can be seated in a row such that two girls are never together?
A
6! 5!
B
2 x 5! x 5!
C
6! x 7P5
D
6! 6!
Answer
6! x 7P5
Explanation
Solution
Since, there is restriction on girls, let us seat the boys first, which can be done in 6! Ways.
(i) x B1 x B2 x B3 x B4 x B5 x B6
For 5 girls there are 7 places shown by “X” above (note that here 2 or more boys can sit together) in which they can be seated in 7P5 ways.
∴ Total ways = 7P5x6!