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Question

The number of surjections from A = {1, 2, 3, …………….. ,n}, n \(\geq\) 2 onto B = {a, b} is

A
nP2
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B
2n2
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C
2n1
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D
None of these
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Solution

The correct option is B 2n2
Number of surjections from A onto B is
nr=1(1)nrnCrrm, provided m n
=r=1n(1)2r2Crrn=(1)12Cn1+(1)02C22n
=2+2n=2n2

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