First slide

Permutations

Question

In how many ways can 5 boys and 5 girls sit in a circle so that no two boys sit together?

Easy

A

5! x 5!
B

4! x 5!
C

$\frac{5! \times 5!}{2}$
D

None of these

Solution

First we fix the alternate position of girls and they arrange in 4! ways and in the five places five boys can be arranged in $^{5} P_{5}$ ways.
$∴$ Total number of ways $= 4! \times^{5} P_{5} = 4! \times 5!$

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