Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys.

Question:

Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys.

Solution:


Five boys can be arranged amongst themselves in 5! ways, at the places shown above.

The three girls are now to be arranged in the remaining four places taken three at a time = 4P3 = 4!

By fundamental principle of counting, total number of ways = 5!×">××4! = 120×">××24 = 2880

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