Question

If A and B have 5 and 4 elements respectively, then number of onto functions from A to B is N then equals

Answer 1

Number of onto function between two sets = Number of distribution of 5 balls into 4 boxes where no ball remains empty.

Here, we can make a quadruplet on 5 is 5 $\to (1,1,1,4)$

Thus, the number of onto functions:

$=\frac{5!}{1!1!1!2!}\times \frac{4!}{3!}$

$=\frac{5!}{2!}\times \frac{4!}{3!}$

$=60\times 4$

$=240$