More permutations and combinations

Six men and three women are standing in a supermarket queue.

How many possible arrangements are there if no two of the women are standing next to each other?

9! = 362880

So we find the number of ways the three women can be seated together, gives (6+1)! x 3! = 30240

362880 - 30240 = 332640

But the answer given is 151200. Can somebody help me out?

Reply 1

Goldenratio

2

That is because you are assuming two women are differentiable, and in this case, I don't see why they should be. It'll be like 6 oranges and 3 apples.

Reply 2

em1n3m

andrewlee89

Six men and three women are standing in a supermarket queue.

How many possible arrangements are there if no two of the women are standing next to each other?

9! = 362880

So we find the number of ways the three women can be seated together, gives (6+1)! x 3! = 30240

362880 - 30240 = 332640

But the answer given is 151200. Can somebody help me out?

O god... THIS QUESTION :s-smilie:

It's from the 06 stats exam that I sat last year. I couldn't do it then, and I still can't =/

Reply 3

andrewlee89

OP

1

yea lol. 06 last year. . .Anybody can nudge me in the right direction? It's getting on my nerves :frown:

Reply 4

OCC++

ur working is wrong because u only take into account the case where 3 women are together side by side.

anyway theres an easier way to see how to do this question.
first arrange the 6 guys . the next step is... clue : (151200/ 6! = (7*6*5)