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Question

Find the number of ways in which 5 boys and 5 girls may be seated in a row so that no two girls and no two boys are together.


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Solution

Find the number of ways as per the given conditions

From the given data, there are 5 boys and 5 girls.

The permutation is an arrangement of r items taken out of n items and the combination is the selection of r items taken out of n items irrespective of the arrangement.

The permutation formula is,

Prn=n!n-r!

So, the number of boys seated in a row in,

P55=5! ways

The girls can fill the 6 space in P56=6! ways.

So,

The number of ways in which no 2 girls and no 2 boys sit together =5!×6!

Hence, the number of ways in which 5 boys and 5 girls may be seated in a row so that no two girls and no two boys are together is 5!×6!.


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