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

Could someone explain, please

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.

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 ?

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