Question

Ih how many ways can 5 boys and 4 girls be arranged on a bench if there are no restrictions

Answer 1

Given:

Number of boys = 5

Number of girls = 4

To find:

The number of ways in which 5 boys and 4 girls be arranged on a bench if there are no restrictions.

Solution:

We have, 5 boys and 4 girls.

Total number of boys and girls:

$5+4=9$

If there are no restrictions, then the total number of ways to arrange 9 persons is:

$^9P_9=\dfrac{9!}{(9-9)!}$

$^9P_9=\dfrac{9!}{0!}$

$^9P_9=\dfrac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{1}$

$^9P_9=362880$

Therefore, the total number of ways to arrange 5 boys and 4 girls is 9! or 362880.