In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together?

Explanation

5 boys can be seated among themselves in ` 5_(P_5)=5 !` Ways.
After this arrangement, we have to arrange the three girls in such a way that in between two girls there atleast one boy.


So the possible places girls can be placed with the `X` symbol given below.

` X ** B** X ** B**X ** B**X ** B**X ** B**X`
`
therefore` There are 6 places to seated by 3 girls which can be done `6_(P_3)` ways.

`therefore` Total number of ways `=5 ! times 6_(P_3)`
`=120 times(6 times 5 times 4)`
`=120 times 120`
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