Question

How many subsets of 100 have exactly 99 elements?

How many subsets of 100 have exactly 98 elements?

How many subsets of 100 have exactly 2 elements?

Answer 1

The number of k-element subsets of a set of n elements is given by

... C(n, k) = n!/(k!(n-k)!)

a) C(100, 99) = 100!/(99!×1!) = 100

b) C(100, 98) = 100!/(98!×2!) = 100*99/2 = 4950

c) C(100, 2) = 100!/(2!×98!) = 4950 . . . . same as (b)