Question

A class in probability theory consists of 3 men and 5 women. An exam is given, and the students are ranked according to their performance. Assuming that no two students obtain the same score, and all rankings are considered equally likely. 1) The number of different possible rankings is a) 3!5! b) 3*5 c) 8! d) 8 2) The probability that women receive the bottom 5 scores is 3. The probability that the top grade and the bottom grade are for men is

Answer 1

1.

There are 3+5 = 8 students.

Any student can get any rank.

Without tie in score, there is no tie in rank.

Number of possible ways of rank is all possible arrangements of 8 ranks i.e. 8!.

Hence, (c) 8!

2.

Number of all possible ranks = 8! = 40320

Women can get bottom 5 scores in 5! = 120 ways

Men can get top 3 scores in 3! = 6 ways

So, required probability is given by

3.

Top and bottom grades can be achieved by 2 men in ways.

Remaining 6 ranks can be filled in 6! = 720 ways

So, required probability is given by