# If $A=\{1,2,3,4\}$ and $B=\{1,2\}$, then the number of onto functions from $A$ to $B$ is

$\begin{array}{1 1} 16 \\ 14 \\ 12 \\ 8 \end{array}$

Toolbox:
• In Onto function all the elements of B should be related.
Ans: (B) =14
case (i)
Any 3 elements of A mapped with one element of B and
one element of A is mapped with the other element of B.
$=^4C_3\times^2C_1=4\times2=8$ onto functions.
case(ii)
Any 2 elements of A mapped with one element of B and
other two elements of A is mapped with the other element of B.
$=^4C_2\times^2C_1=3\times2=6$ onto functions.
Total $8+6=14$
answered Apr 28, 2013