Discussion Forum

Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets A x B  having 3  or more elements is 

Answer:

Explanation:

Given  , n (A)=2, n(B)= 4

 $\therefore$  n(A X B)=8

 The number of subsets of AxB having 3 or more elements

  = $^{8}C_{3}+^{8}C_{4}+.....+^{8}C_{8}$

  =   $(^{8}C_{0}+^{8}C_{1}+^{8}C_{2}+^{8}C_{3}.....+^{8}C_{8})-(^{8}C_{0}+^{8}C_{1}+^{8}C_{2})$

  $\therefore$ 2ⁿ= $^{n}C_{0}+^{n}C_{1}+.....+^{n}C_{n}$

  $=2^{8}-^{8}C_{0}-^{8}C_{1}-^{8}C_{2}$

  =256-1-8-28=219