It is required to seat 5 men and 4 women in a row so that the women occupy the even places.

Question:

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

Solution:

5 men and 4 women are to be seated in a row such that the women occupy the even places.

The 5 men can be seated in 5! ways. For each arrangement, the 4 women can be seated only at the cross marked places (so that women occupy the even places).

                                                                                             $\mathrm{M} \times \mathrm{M} \times \mathrm{M} \times \mathrm{M} \times \mathrm{M}$

Therefore, the women can be seated in 4! ways.

Thus, possible number of arrangements = 4! × 5! = 24 × 120 = 2880

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