2. A small ice cream company has 8 flavors of ice cream, 3 of which are sorbets
ID: 3201980 • Letter: 2
Question
2. A small ice cream company has 8 flavors of ice cream, 3 of which are sorbets and 5 of which are dairy ice cream. Assume all flavors are equally likely to be chosen, repetition is not allowed, and the order of the flavors does not matter. (Write the formula used)
(a) How many ways are there to pick three flavors of ice cream?
(b) How many ways are there to pick three flavors of ice cream, where one is a sorbet and two are dairy?
(c) What is the probability of randomly picking three flavors where two are sorbet and one is a dairy?
(d) If someone has decided to pick dairy ice cream, how many ways are there to pick three flavors?
(e) What is the probability of randomly picking two flavors of ice cream that are both diaries?
Explanation / Answer
(a) There are C(8, 3) ways = 56 ways
(b) One sorbet and two dairies can be chosen in C(3, 1) * C(5, 2) = 3 * 10 = 30 ways
(c) Two sorbets and 1 dairy can be chosen in C(3, 2) * C(5, 1) = 3 * 5 = 15 ways
Probability = 15/56
(d) Three flavors can be picked out of 5 in C(5, 3) ways = 10 ways
(e) Two flavors out of 8 can be chosen in C(8, 2) ways = 28 ways
Two dairies can be chosen out of 5 dairies in C(5, 2) = 10 ways
Probability = 10/28 = 5/14
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