Solve the problem.
-If a given set has nine elements, how many of its subsets have at least five elements?
A)256 subsets
B)130 subsets
C)32 subsets
D)255 subsets

Question

Quizplus · Accepted Answer

The number of subsets with at least five elements is equal to the total number of subsets minus the number of subsets with four or fewer elements. The total number of subsets of a set with n elements is 2^n, so the total number of subsets of a set with nine elements is 2^9 = 512. The number of subsets with four or fewer elements is equal to the sum of the number of subsets with zero elements, one element, two elements, three elements, and four elements. The number of subsets with zero elements is 1, the number of subsets with one element is 9, the number of subsets with two elements is 36, the number of subsets with three elements is 84, and the number of subsets with four elements is 126. Therefore, the number of subsets with four or fewer elements is 1 + 9 + 36 + 84 + 126 = 256. Therefore, the number of subsets with at least five elements is 512 - 256 = 256.

Solve the Problem. -If a Given Set Has Nine Elements, How Many of How