Suppose that Y takes on the values 0 1 2 3 each with probabi

Suppose that Y takes on the values {0, 1, 2, 3}, each with probability 1/4. Take a random sample of 5 numbers from this distribution. In how many possible samples can the sum of the five numbers (Y1 + Y2 + Y3 + Y4 + Y5) equal to 1?

Solution

Note that for the sum to be equal to 1, then there must be exactly four 0s, and exactly one 1.

There\'s no other way about it.

Thus, there are these 5 ways:

{Y1, Y2, Y3, Y4, Y5} = {0,0,0,0,1}, {0,0,0,1,0}, {0,0,1,0,0},{0,1,0,0,0},{1,0,0,0,0} [ANSWER, 5 WAYS]