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Total number of ways of arranging 7 boys and 5 girls in a row such that no two girls come together

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First, let us consider the order of the boys, ignoring the placement of the girls. Given 7 boys, there are 7!=5040

Without placing girls yet, the row of boys would look like this:

_ B _ B _ B _ B _ B _ B _ B _

Note that there are 8 spaces in which to place girls. We can’t have more than one girl per space. There are 8x7x6x5x4=6720 placements of girls in the spaces.

Multiplying the number of arrangements of boys with the number of placements of girls, our answer is 5040x6720=33868800.

Posted by

Ravindra Pindel

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