Question

If four distinct sets of four blocks are present, and seven are randomly removed, what is the expected number of complete sets remaining?

a) 0
b) 1
c) 2
d) 3

Answer 1

The expected number of complete sets remaining is 10.

Step-by-step explanation:

To find the expected number of complete sets remaining, we first need to calculate the probability of a set being removed. Each set of four blocks has a total of 4! = 24 possible arrangements. If seven blocks are randomly removed, there are 10 blocks left. The total number of ways to choose 7 blocks out of 10 is given by the combination formula C(10, 7) = 120. Since each selection of 7 blocks can remove at most 2 complete sets, we can calculate the expected number of complete sets remaining by multiplying the probability of a set being removed (2/24) by the total number of selections (120). So the expected number of complete sets remaining is (2/24) * 120 = 10.