Question

Three men and three women stand in a line. find the number of different ways in which they can be arranged

(iii) if no man stands next to another man

Answer 1

6P6 are the total arrangements

Answer 2

Yes but what if no man stands next to another man?

Answer 3

Oh i didnt see that part

Answer 4

We can either have:

M W M W M W

or

W M W M W M

Since there are 3 women, the number of ways we can order them is 3*2*1 = 6. Same for the men since there are 3 men. 6 ways for the women * 6 ways for the men gives 36 ways to arrange them. The two configurations above makes 72.

Answer 5

The answer at the back is 21

Answer 6

im trying to see if ive over thought the problem....but 21 seems like too few.

Answer 7

I'm sure that's the answer... but I don't know how to get 21. I tried combinations with if all men were next to eachother, which would get you the 36... but this is if no man was next to eachother..

Answer 8

are you counting the M/W as different people? LIke M1, M2, M3, W1, W2, W3? When i learned this, it was an unwritten rule that you can always distinguish between people. If you arent doing this, it would explain the difference in our answers.

Answer 9

Oh, yes, you can distinguish, but the answer is clearly 21... not sure how to get it

Answer 10

ive listed more than 21 possible combinations, and there are a lot more. This was only considering the arrangement M W M W M W, and in each picture, the men change order in each line, while the way the women are ordered changes from picture to picture. 21 is too small of an answer, unless im not reading the question correctly.

Answer 11

Hmmm I don't know then... Thanks for your help though! I'll need to think this one through or ask a statistician...

Answer 12

I'll give you a medal for trying :)

Answer 13

yeah, the question isnt worded properly if 21 is indeed the correct answer.

Answer 14

What about M W M W W M types of combinations?
We could also include those in the calculations.

Answer 15

yes

Answer 16

2*3P3*3P3 =72