Question

A set contains 9 elements. Then the number of subsets of the set which contains at most 4 clements is

• A. 32
• B. 64
• C. 128
• D. 256
• E. 512

Answer 1

The Correct Option is D

We are given a set with 9 elements, and we need to find the number of subsets of the set that contain at most 4 elements.

The total number of subsets of a set with \(n\) elements is given by: 

\(2^n\)

For a set of 9 elements, the total number of subsets is:

\(2^9 = 512\)

Now, we need to calculate the number of subsets that contain at most 4 elements. This means we need to count subsets containing 0, 1, 2, 3, and 4 elements. We use the combination formula to find the number of subsets of each size:

• Number of subsets with 0 elements: \(C(9, 0) = 1\)
• Number of subsets with 1 element: \(C(9, 1) = 9\)
• Number of subsets with 2 elements: \(C(9, 2) = 36\)
• Number of subsets with 3 elements: \(C(9, 3) = 84\)
• Number of subsets with 4 elements: \(C(9, 4) = 126\)

Now, we sum these values to find the total number of subsets containing at most 4 elements:

\(1 + 9 + 36 + 84 + 126 = 256\)

The number of subsets of the set that contain at most 4 elements is 256.