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.

a) 3628800, b) 720.

Step-by-step explanation:

Since we have given that

Number of men = 6

Number of women = 4

So, Total number of persons = 6+4 =10

(a) How many different rankings are possible?

Using "fundamental theorem of counting", we get that

there are different ranking which is 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.

Number of ranking possible if only 3 students are selected is solved with the help of "Permutations":

Hence, a) 3628800, b) 720.

$15 each

step-by-step explanation:

$45/3 children= $15 each