Question

How many subsets of exactly two elements does a set of five elements have?

A.10
B.26
C.7
D.32

Answer 1

A. 10

Explanation:

Answer 2

Option: A is the correct answer.

A. 10

Explanation:

We know that the number of subsets of exactly ''r'' elements that is formed by the help of n elements is calculated by:

`n_C_r`

Since here we have to chose 2 elements out of the 5 elements in order to form a subset.

Hence, we have: n=5 and r=2

Hence, the number of subsets are:

`5_C_2=(5!)/(2!* (5-2)!)\\\\\\5_C_2=(5!)/(3!* 2!)\\\\\\5_C_2=10`

Hence, the number of subsets are:

10