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Question

Write the formula to find the number of onto functions from set A to set B.


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Solution

Formula to find the number of onto functions from set A to set B.

Onto function

Let the number of elements in set A be n.

Let the number of elements in set B be m.

Total number of functions from A to B are,

mn

The formula to determine the number of functions that is onto is given by:

mn1mm1n+2mm2n-3mm3n+.....-m1m1n

When, n<m, the number of onto functions is zero.

When, n=m, the number of onto functions is m!.

Therefore, the number of onto function from A to B can be find with the formula,

mn1mm1n+2mm2n-3mm3n+.....-m1m1n


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