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If A and B two sets containing 2 element...

If A and B two sets containing 2 elements and 4 elements, respectively. Then, the number of subsets of `A xx B` having 3 or more elements, is

A

256

B

220

C

219

D

211

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `n(A) =2, n(B)=4`
` therefore n(A xx B)=8`
The number of subsets of `A xx B` 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 2^(n) =""^(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`
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