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Number of Elements in a Cartesian Product

How many func...

Question

How many functions can be defined from a set $A$ containing $5$ elements to a set $B$ having $3$ elements $?$ How many of these are onto functions $?$

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Solution

Total number of function can be formed $= 3^{5}$

Total onto function can be formed $= 3^{5} - 3 - 3 \times 2^{5} = 144$

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