Question

Four men and four women have just six tickets in one row to the theater. In how many ways can they sit if the first person in the row is a woman and the people alternate woman,men?

Answer 1

They can sit in `576` ways.

Explanation:

As there are six seats in a row and the first person in the row is a woman and the people alternate woman, men, the possibility is

`WMWMWM` in that order.

Now as we four women, three seats for women can be filled in `color(white)X^4 P_3=24` ways

and similarly as we four men, three seats for men can be filled in `color(white)X^4 P_3=24` ways

Hence, total `24xx24=576` permutations.