Probablity - Permutations with Alernate Seating

The places can be filled up starting with a man or a woman
and for each possibility it can be filled up in the way stated below.
_ _ _ _ _ _
3*3*2*2*1*1=36

so total no of ways=36*2

hope it helps.

Hi!

This question is tricky. I hope I understand it correctly.

They must alternate, so we have two possibilities:
- Men take even seats and women take odd seats
- Women take even seats and men take odd seats

3 men can take 3 seats. Therefore, they can be seated in 3! ways.
3 women can take 3 seats. Therefore, they can be seated in 3! ways.

Hence, 3 men and 3 women can be seated in 6 seats in x ways, if they must alternate.
x = 2*3!*3! = 72

Hope it helps!
Best,
Maciek