Question

from a school 5 boys and 4 girls has been selected for competition.how many ways photographs can be taken placing them in a row such that no two girls remain together?

Answer 1

First take the 5 boys and arrange them.

It can be done in 5P5 ways.

Now, we have to arrange 4 girls such that no two girls stay together.

So we have to insert one girl in each position between boys. There can be 6 positions as shown below.

G B G B G B G B G B G

So we have to arrange 4 girls in 6 positions. It can be done in 6P4 ways.

$Total \: ways= {}^5P_5 × {}^6P_4 \\ \\ = \frac{5!}{(5 - 5)!} \times \frac{6!}{(6 - 4)!} \\ \\ = \frac{5!}{0!} \times \frac{6!}{2!} \\ \\ = 120 \times 360 \\ \\ = \boxed{43200 \: ways}$

Total ways = 43200

Answer 2

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