Let `A={1,2,..., n}` and `B={a , b` }. Then number of surjections from `A` into `B` is nP2 (b) `2^n-2` (c) `2^n-1` (d) nC2

Explanation

Given that, `A={1,2,3, ldots, n}` and `B={a, b}`.


We know that, if `A` and `B` are two non-empty finite sets containing `m` and `n` elements respectively, then the number of surjection from `A` into `B` is


`.^{n} C_{m} times m !`, if `n geq m`


0 , if `n

Here, `m=2`


`therefore` Number of surjection from `A` into `B` is



`.^{n} C_{2} times 2 !=frac{n !}{2 !(n-2) !} times 2 !`


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