A class in probability theory consists of 6 men and 4 women. An exam is given an

Question

A class in probability theory consists of 6 men and 4 women. An exam is given and the students are ranked according to their performance knowing their gender but without knowing their names. Assuming that students obtains a different score (i.e. no two students will obtain the same score).
(a) How many different rankings are possible?
(b) If only 3 students are selected at random, how many different rankings are possible in this case? Use a tree diagram to find the list of all possible rankings in this case.

Explanation / Answer

a) Number of different rankings possiblr are = 10! = 3628800

b) Number of different rankings possible if 3 students are selected = 10P3 = 10! / 7! = 720

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