Combinatorics problem-Slot method

[dddanny2006]

Source-Princeton Review
The acting group is putting a play that has 4 female and 3 male roles.There are 5 women and 5 men. How many ways the roles can be assigned?


Correct Answer is 7200

My method.

Women 5*4*3*2 =5--------------Order doesnt matter
4!


Men 5*4*3 =10-----------Order doesnt matter
3!


Therefore 5*10=50

Please tell me my mistake.

[RonPurewal]

Hi,
As I mentioned here --
post94482.html#p94482
-- we can't continue to answer posts with titles that don't conform to the forum rules.

Please read the forum rules -- first thread in every folder -- and then re-post your question with an appropriate title (i.e., based on the first few words of the question).

Thanks.