find the number of ways in which 5 ladies and 5 gentlemen may be seated in a row so that no two ladies are together.

In this problem why we use 11 places although there are only 10 persons?

Let the gentlemen be seated firstly. This can be done in 5 ! ways.

For each arrangement, the 5 ladies can be seated only at the cross marked places.

GGGGG

There are 6 cross marked places and the 5 ladies can be seated in

therefore, required no. of ways 

  • 8
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