The U.S Olympic gymnastics team for the 2016 Rio Games comprised five women and five men. In how many ways can this group of athletes arrange themselves in a row for a group picture if:

Question

The U.S Olympic gymnastics team for the 2016 Rio Games comprised five women and five men. In how many ways can this group of athletes arrange themselves in a row for a group picture if:
a) There is no restriction
b) The men stand together in a group and the women stand together in a group?
c) The men and women must occupy alternate positions?

a) The 5 women + the 5 men = 10
P(10,10) =10!

b) Women : P(5,5) Men: P(5,5)
p (5,5) * p (5,5) = 120*120=14400

c) p(5,5)*p(5,5)=120*120=14400

Reiny · Answer

Even though your answer is correct, I would argue c) as follows: from left to right MWMWMW... = 5*5*4*4*3*3*2*2*1*1 = 5! * 5! = 14400