SOLUTION: Three men and four women are to line up for a picture with the three men in the middle. How many ways can this be done? (Assume there are two women on each side of the group of men

Algebra ->  Permutations -> SOLUTION: Three men and four women are to line up for a picture with the three men in the middle. How many ways can this be done? (Assume there are two women on each side of the group of men      Log On


   

Question 950045: Three men and four women are to line up for a picture with the three men in the middle. How many ways can this be done? (Assume there are two women on each side of the group of men)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
1 2 3 4 5 6 7   <-positions
W W M M M W W   <-gender

Choose the woman to go in position 1 as any one of the 4 women.
Choose the woman to go in position 2 as any one of the 3 remaining women.
Choose the woman to go in position 6 as either one of the 2 remaining women.
Choose the woman to go in position 7 as the only 1 remaining women.
Choose the man to go in position 3 as any one of the 3 men.
Choose the man to go in position 4 as any either one of the 2 remaining men.
Choose the man to go in position 5 as the 1 remaining man.

Answer: (4*3*2*1)*(3*2*1) = 4!*3! = 24*6 = 144

Edwin