SOLUTION: 7 awards are received; Jef (M), Ka (F), Lyle (M), Mai (F), Norm (M), Pat (F), and Sam (F). In how many ways can the awards alternate between men and women with a woman going firs

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Question 1201481: 7 awards are received; Jef (M), Ka (F), Lyle (M), Mai (F), Norm (M), Pat (F), and
Sam (F). In how many ways can the awards alternate between men and women with a
woman going first?
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
7 awards are received; Jef (M), Ka (F), Lyle (M), Mai (F), Norm (M), Pat (F),
and Sam (F). In how many ways can the awards alternate between men and women
with a woman going first?
Let the order be F1 M1 F2 M2 F3 M3 F4

Choose F1 4 ways.
Choose M1 3 ways.
Choose F2 3 ways.
Choose M2 2 ways.
Choose F3 2 way.
Choose M3 1 way.
Choose F4 1 way.

(4)(3)(3)(2)(2)(1)(1) = 144

Edwin
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

HINT to those unhappy students who are obliged to read this formulation:


        It is not about alternating awards.

        It is about alternating men and women in a line.

        Awards are introduced in this problem with the only goal to confuse you.



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