SOLUTION: Suppose a City Council consist of 4 men and 5 women. a. In how many ways can the City Council members be lined up for a group picture? I'm not sure if I did this right, but he

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Suppose a City Council consist of 4 men and 5 women. a. In how many ways can the City Council members be lined up for a group picture? I'm not sure if I did this right, but he      Log On

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Question 75963: Suppose a City Council consist of 4 men and 5 women.
a. In how many ways can the City Council members be lined up for a group picture?
I'm not sure if I did this right, but here is how I approached this problem.
9x8x7x6x5x4x3x2x1=362,880
I was confused on these.
b. In how many ways can they be lined up if the men and women must alternate?
c. In how many ways can they be lined up with the men together and the women together?
d. In how many ways can they be arranged if two rows are used with the women in the front row and the men in the back row?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Your answer to (a) looks correct.
As to (b), the only way the men and women can alternate is if
women are at both ends. If you try putting a man at one end, you
end up putting 2 women together. So it goes
W M W M W M W M W
There are 5 possible ways to put a woman in the 1st position
There are 4 possible ways to put a man in the 2nd position
There are 4 possible ways to put a woman in the 3rd position
There are 3 possible ways to put a man in the 4th position
There are 3 possible ways to put a woman in the 5th position
There are 2 possible ways to put a man in the 6th position
There are 2 possible ways to put a woman in the 7th position
There is 1 possible way to put a man in the 8th position
There is 1 possible way to put a woman in the 9th position
The product of all the possibilities is the answer
5%2A4%2A4%2A3%2A3%2A2%2A2%2A1%2A1+=+2880 answer
(c) If the women and men are grouped together, It looks like
4%2A3%2A2%2A1+=+24 possible ways to arrange the men and
5%2A4%2A3%2A2%2A1+=+120 possible ways to arrange the women
All the possible combos is the product 24%2A120+=+2880
But this isn't the final answer. For every combo, the group
of men can be on the left or the right, so I think the
correct answer is 2%2A24%2A120+=+5760
And (d) is the 24%2A120+=+2880 because you can't interchange the
groups of men and women.