In how many ways can 5 boys and 3 girls sit in a row so that... | MATH - DEFINITION OF PERMUTATION, NUMBER OF PERMUTATIONS WITH OR WITHOUT REPETITION | SolveeIt | Solveeit

Today, August 18

Question

In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together.

A

$5! \times 3!$

B

$4P_{3} \times 5!$

C

$6P_{3} \times 5!$

D

$5P_{3} \times 3!$

Answer

$6P_{3} \times 5!$

Explanation

Solution

Since the 5 boys can sit in $5\mspace{6mu}!$ ways. In this case there are 6 places are vacant in which the girls can sit in $6P_{3}$ ways. Therefore required number of ways are $6P_{3} \times 5\mspace{6mu}!$ .