1 The Asian student club at UC Merced has 43 members In how

1) The Asian student club at UC Merced has 43 members. In how many ways can three members be randomly chosen to receive funding to attend a conference on artificial intelligence in Orlando, Florida?

Answer: 43C3 = 12341

2) In the Asian Student Club at UC Merced which has 43 members, 18 of the members of the members belong to the Hmong nationality. What is the probability that all three of the students chosen in problem 1 above are Hmong nationality?

Solution

1)

The number of ways of selecting m people out of a group of n peopleis given by C(n,m)

In this problem there is a group of 43 members, out of which three members are to be chosen to recieve funding.

Thus the number of ways will be given by , C(43,3) = 43!/(40!3!) = 12341

2)

In this problem, there is a subgroup of Hmong nationality among Asian Student club consisiting of 18 members. So here favourable cases would be selecting 3 members out of the 18 members of subgroup of Hmong Nationality.

Favourable cases = C(18,3) = 816

Sample space will contain all cases whether favourable or not.

Total number of cases = C(43,3) = 12341

Probability that all of the three chosen students chosen belong to Hmong Nationality = 816/12341 = 0.066