A class of probability theory consists of 6 male and 4 female students. Assume no two students obtain the same score.

a) If all students are ranked according to their performance how many different rankings are possible?

b) If the male and female students are ranked among themselves how many different rankings are possible?

The number of different rankings possible are = 10! = 3,628,800

The total number of ways If the male and female students are ranked among themselves are 17280.

Step-by-step explanation:

Consider the provided information.

A class of probability theory consists of 6 male and 4 female students.

Part (a) If all students are ranked according to their performance how many different rankings are possible?

Here the total number of students are:

6+4=10 students

So, there are 10! possible rankings

Hence, the number of different rankings possible are = 10! = 3,628,800

Part (b) If the male and female students are ranked among themselves how many different rankings are possible?

If all of them ranked among themselves then the possible number of ranking for man are 6! = 720

The possible number of ranking for female are 4! = 24

Therefore, the total number of possible ranking are = 720*24 = 17280

Hence, the total number of ways are 17280.