Question

Given the b= [1,2,3,4}, how many subsets have exactly two elements

Answer 1

Answer:

6

Step-by-step explanation:

We are given that a set b={1,2,3,4}

We have to find number of subsets which contain exactly two elements.

Combination formula

$nC_r=\frac{n!}{r!(n-r)!}$

We have n=4, r=2

Using the combination formula

$4C_2=\frac{4!}{2!(4-2)!}$

$4C_2=\frac{4\times 3\times 2!}{2!2!}$

$4C_2=\frac{4\times3}{2\times1}$=6

Subsets of given set which contain exactly two elements={1,2},{2,3},{3,4},{1,3},{1,4},{2,4}

Hence, 6 subsets of  a set which contain exactly two elements.

Answer 2

6

{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}