A foreign student club lists as its members 2Canadians, 3 Japanese, 5 Italians, and 2 Germans. Ifa committee of 4 is selected at random, find the probability that(a) all nationalities are represented;(b) all nationalities except Italian are represented.

Step-by-step explanation:

(a)

Total number of members are (2 + 3 + 5 + 2) = 12.

From these 12 members 4 can be chosen in ways.

All the nationalities will be there only when one from each nationality will be there.

Hence, the required answer is .

(b)

There will be no Italians, hence all 4 should be chosen from (12 - 5) = 7 people.

From, 7 people, 4 can be chosen in ways.

Hence, in this case, the probability will be .