Question

The total number of functions,
$f:\{1,2,3,4\}\to \{1,2,3,4,5,6\}$ such that $f(1)+f(2)=f(3)$, is equal to :

• A. 60
• B. 90
• C. 108
• D. 126

Answer 1

Answer: (B)

$A=\{1,2,3,4\}$
$B=\{1,2,3,4,5,6\}$
Here $f(3)$ can be $2,3,4,5,6$
$f(3)=2,(f(1),f(2))\to (1,1)\to 6$ cases
$f(3)=3,(f(1),f(2))\to (1,2),(2,1)$
$\to 2\times 6=12$ cases
$f(3)=4,(f(1),f(2))\to (1,3),(3,1),(2,2)$
$\to 3\times 6=18$ cases
$f(3)=5,(f(1),f(2))\to (1,4),(4,1),(2,3)$
$(3,2)$
$\to 4\times 6=24$ cases
$f(3)=6,(f(1),f(2))$
$(1,5),(5,1),(2,4),(4,2),(3,3)$
$\to 5\times 6=30$ cases
Total number of cases $=6+12+18+24+30=90$