Find the numbers of ways in which 5 girls and 5 boys can be arranged in a row if no two boys are together.

Explanation

In this example, there is no condition for arranging the girls. Now, 5 girls can be arranged in 5! Ways
XGXGXGXGXGX
When girls are arranged, six gaps are generated as shown above with 'X'.
Now, boys must occupy the places with 'X' marked, so that no two boys are together.
Therefore, five boys can be arranged in these six gaps inn `.^(6)P_(5)` ways.
Hence, total number of arrangement is `5!xx.^(6)P_(5)`