In how many ways can we fill seven numbered seats with three

Question

In how many ways can we fill seven numbered seats with three men and four women by selection from six men and five women?

stolyar · Answer

First select 3 men and 4 women = 6C3*5C4=100 selections
Each seven-person selection should be placed in 7 places = 7!= 5040

total 504000

prashant · Answer

Stolyar, since the women are all same and men are all same, the multiplication factor should be 

7!/3!*4! = 35 and therefore the total ways should be 100*35 = 3500

What do you think?

Konstantin Lynov · Answer

Could someone explain, please

kpadma · Answer

Pradhant

I couldn't understand when you said "since the women are all same and men are all same, the multiplication factor should be 

7!/3!*4! = 35 and therefore the total ways should be 100*35 = 3500"

Could you please elobarate on your explanation.
BTW: I got the same answer as Saylor. But, he agreed you are right.

Sameer · Answer

I am not sure of the explanation too. In any such questioon about men/women, we NEVER assume people are same. The explanation for 7!/(4!*3!) would be ok if there were red and white balls. However, for men/women, original solution of Stolyar seems correct. Comments ?

prashant · Answer

The question says that there are 6 men and 5 women, and we have to choose 3 men and 4 women. The only two "categories" of choice are Men and Women - woman 1 is sitting in chair 1 is not different from woman 2 sitting in chair 1. Therefore, in order to arrange these choices into 7 chairs, the only way the arrangements will differ is if a certain chair is occupied by a man or a woman. Therefore, the number of arrangements for 3 men and 4 women are (3+4)!/3!*4! = 7!/3!*4! = 35 Multiply this by the number of ways in which the choices of men and women were made and you get the answer = 100*35=3500 Hope this helps - I'm not a tutor like Akamai, but I try my best

In how many ways can we fill seven numbered seats with three

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