A tea shoppe serves 12 different flavors of tea. 4 customers each order a cup of tea. Assuming that
Montenovofe
Answered question
2022-07-12
A tea shoppe serves 12 different flavors of tea. 4 customers each order a cup of tea. Assuming that each customer's choice is completely random and is independent of any other customer's selection: 1) what is the probability that 3 different flavors are selected by the 4 customers (e.g:: if letters A-L represent flavors, AABC)? 2) what is the probability that only 2 different flavors are selected by these 4 customers (e,g: AABB or AAAB)? 3) what is the probability that 2 students choose 1 flavor and the other 2 choose another flavor (e.g: AABB)?
Answer & Explanation
lofoptiformfp
Beginner2022-07-13Added 16 answers
If the four customers select three different flavors, then two of the four customers choose one of the 12 flavors, a third customer chooses one of the remaining 11 flavors, and the fourth customer chooses one of the remaining 10 flavors, which can be done in ways. The number of ways three of the four customers can choose one of the 12 flavors and the fourth chooses one of the remaining 11 flavors is
The number of ways one pair selects one of the 12 available flavors while the other pair chooses one of the remaining 11 flavors is
The factor of 1/2 is necessary since the same selection results when the first pair chooses flavor A then the second pair chooses flavor B as when the second pair select flavor B then the first pair chooses flavor A. Thus, the number of ways that the customers can select two different flavors is
Hence, the total number of ways of selecting either two or three different flavors is