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Question

If n(A)=43,n(B)=51 and n(AB)=75, then n[(AB)(BA)] is equal to

A
53
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B
45
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C
56
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D
66
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E
46
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Solution

The correct option is D 56
Given, n(A)=43,n(B)=51 and n(AB)=75
Now, by addition theorem of probability,
n(AB)=n(A)+n(B)n(AB)
=43+5175=19
Now, n[(AB)(BA)]
=n(AB)n(AB)
=7519=56

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