Question

Cole, Matthew and Chris have a jelly bean collection. together they have 36 flavors. If they decide to randomly choose 3 flavors, what is the probability that the 3 they choose will consist of each of their favorite flavors? Assume they have different favorites. express your answer as a fraction

Answer 1

1/46656

Step-by-step explanation

Let A, B and C represent Cole, Matthew and Chris respectively.

Number of flavors, n(s) = 36

Since they randomly chose 3 flavors, so each of them chooses 1 flavour,

⇒ P(A) = P(B) = P(C) = 1/36

The probability that the 3 they choose will consist of each of their favorite flavors =

P(A) x P(B) x P(C) -----Independeent events

1/36 x 1/36 x 1/36

= 1/46656

The probability that the 3 they choose will consist of each of their favorite flavors is 1/46656