Question

Permutation or combination?
seating 5 men and 5 women alternately in a row, beginning with a woman

Answer 1

since we have to start with a woman...one is already placed. so we are left with 4 women and 5 men. which gives us the permutation 5! * 4! = 2880

Answer 2

Does the order matter? Then which is it?

Answer 3

meaning??

Answer 4

In which is the order important? Permutations or combinations?

Answer 5

Order doesn't matter. We just have select and then arrange them. Permutation is basically combinations + arrangement.

Answer 6

So if I have understood correctly, we are calling this a permutation and the number of combination + arrangements is given by 5! * 4!

Answer 7

Exactly!

Answer 8

Thanks. So if the first position wasn't anchored to seating a woman first, then the number of permutations is 5!*5!?

Answer 9

We have 5 choices for the first seat, 5 for the second, 4 for the third, 4 for the fourth, 3 for the fifth, 3 for the sixth, 2 for the seventh, 2 for the eighth, 1 for the ninth, 1 for the tenth
Result: 5!5!

Answer 10

Thanks! I am going to go work on some of these problems - appreciate it.

Answer 11

So now that I have actually studied this problem a little more, the answer given previously is incorrect. It is actually two separte problems disguised as one. The fact that there is altenation of seating with exactly the same number of chairs as people to be allocated makes it interesting. Women can only beseated in odd numbered chairs, 1, 3, 5, 7, and 9. Men can sit in even numbered chairs, 2, 4, 6, 8, and 10. This results in two problems P(5,5) and P(5,5) one set of combintations for women another for men. 5! x 5! = 14,400 permutations.

If we had only the first seat anchored and the other 9 that we could assign to either men or women the problem is 5 x P(9,9) = 1,814,400.

Answer 12

I don't believe your answer is right. The men and women must alternate seats. So you never have 9 choices for any seat. The 5!5! answer is correct.