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

Explanation

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



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


`0 text { if } {m}


Here, number of elements in `A=4=m`


Number of elements in `B=2=n`


So, `m>n`


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