Let `A={1,\ 2,\ 3,\ 4}` and `B={a ,\ b}` be two sets. Write total number of onto functions from `A` to `B` .

Explanation

`A={1,2,3,4} text { and } B={a, b}`



When two sets `A` and `B` have `m` and `n` elements respectively, then the number of onto function from `A` to `B` is,


`sum_{m=1}^{n}(-1)^{m}{n} C_{m} n^{m}`, if `m geq n`


And 0 if `{m}<{n}`


`Rightarrow` Number of elements in `{A}({m})=4`


`Rightarrow` Number of elements in `B({n})=2`


So, `m>n`


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