Question

A={1,2,3,4,5,6,7,8,9,10}. then the number of subset of A containing two or three elements is-?

Answer 1

Given there are 10 elements.

Number of subset of A containing 2 or 3 elements  = 10c2 + 10c3

                                                                                      = 45 + 120

                                                                                      = 165.

Answer 2

Given,
A={1,2,3,4,5,6,7,8,9,10}.
n(A) =10

Number of subsets containing 2 or 3 elements = 10C2+10C3

= 10!/(8! × 2!) + 10! /(7! × 3!)

= (10 x 9) / 2 + (10 x 9 x 8) / (3×2)

= 45 + 120

= 165