Let A and B be two sets containing four and two elements, respectively. Then, the number of subjects of the set `A xx B`, each having atleast three elements is

Options

A. 275
B. 510
C. 219
D. 256

Answer

C

Explanation

We have,
n(A) = 4 and n(B) = 2
`therefore n(A xx B) = n(A) xx n(B) = 4xx2=8`
Required number of subsets = `.^(8)C_(3)+.^(8)C_(4)+.^(8)C_(5)+...+.^(8)C_(8)=(underset(r=0)overset(8)Sigma.^(8)C_(r))-(.^(8)C_(0)+.^(8)C_(1)+.^(8)C_(2))=2^(8)-(1+8+28)=219`