Question

Let $E=\{1,2,3,4\}$ and $F=\{1,2\}$. Then the number of onto functions from $E$ to $F$ is

• A. $14$
• B. $16$
• C. $12$
• D. $8$

Answer 1

Answer: (B)

$16$

The total number of ways of distributing $(1,2)$ considering them as 2 objects among $(1,2,3,4)$ considering them as 4 people is equal to total no. of Onto functions from E to F.

There can be two ways of distributing $(1,2),$

Either we give both to one people

Or give $1$ to one people and $2$ to another.

So, Total no. of ways $=4\times 1{+}^4{C}_2\times 2=16$