Question

A class in probability theory consists of 6 men and 4 women. An examination is
given, and the students are ranked according to their performance. Assume that no
two students obtain the same score.

(b) If the men are ranked just among themselves and the women just among themselves,
how many different rankings are possible?

why the answer is not 4!*6!*2! ???????follwo the comment please

Answer 1

According to the given condition, there are two ranking schemes, one is only for men and another is only for women.

In that case, number of different rankings possible = 6! x 4!

= 17,280

4! x 6! x 2! is the answer when the condition is as follows: Either all men scored higher than all women or all women scored higher than all men. In this case, the answer is 6!x4! + 4!x6! = 4! x 6! x 2!. But here, that is not the case. Here, men have a ranking from 1 to 6 and women have another ranking from 1 to 4. So, the number of ranking possible = Number of rankings among men x Number of rankings among women = 6! x 4!