Question

In how many ways can three men and three women be seated in a row of six seats for each of the following arrangements?


(a) The women are to be seated together.

(b) The men and women are to be seated alternately by gender.

Answer 1

(a) The women are to be seated together. This means they occupy either seats {1,2,3}, {2,3,4}, ..., {4,5,6}. That is, there are four possibilities. Thus, there are 4 * 3! * 3! ways for the women and men to be seated.

(b) Ok, suppose every odd numbered seat is for men, and every even numbered seat is for women. Then, the first odd seat can seat 1 of the 3 men, the second odd set can seat 1 of the 2 remaining men, and the last odd seat can seat the last remaining man. Likewise for the women. Thus, there are 3! * 3! ways to seat them when assigning men to odds and women to evens. However, another valid arrangement is to seat the men on the even numbered seats instead. Thus, there are 2*3!*3! ways to seat them.

Answer 2

@queelius THANK! YOU! so much!!

Answer 3

No problem. Do you want to discuss the solution?

Answer 4

@queelius no everything you have typed I understood thank you I was super stuck on this one and now I can finish the rest of my home work thanks ;)

Answer 5

Good! See ya around.