How many subsets of exactly two elements does a set of five elements have? A.10 B.26 C.7 D.32

Question

asked Jul 10, 2018 214k views

2 Answers

Parnas · Answer 1 · 2018-07-16T06:02:32+0000

Option: A is the correct answer.

A. 10

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