Return to Example 1.8.6. Let S be the larger sample space (first method of choosing) and let S' be the smaller sample space (second method). For each element s' of S', let N(s') stand for the number of elements of S that lead to the same boxful s' when the order of choosing is ignored.
a. For each s' ∈ S', find a formula for N(s'). Let ni stand for the number of items of type i in s' for i = 1, . . . , 7.
b. Verify that ∑s'∈S' N(s') equals the number of outcomes in S.