Question

The total number of functions,
$f :\{1,2,3,4\} \rightarrow\{1,2,3,4,5,6\}$ 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)) \rightarrow(1,1) \rightarrow 6 $ cases
$ f (3)=3,( f (1), f (2)) \rightarrow(1,2),(2,1) $
$ \rightarrow 2 \times 6=12 $ cases
$ f (3)=4,( f (1), f (2)) \rightarrow(1,3),(3,1),(2,2)$
$\rightarrow 3 \times 6=18 $ cases
$ f (3)=5,( f (1), f (2)) \rightarrow(1,4),(4,1),(2,3)$
$ (3,2) $
$ \rightarrow 4 \times 6=24 $ cases
$ f (3)=6, ( f (1), f (2))$
$ (1,5),(5,1),(2,4),(4,2),(3,3)$
$ \rightarrow 5 \times 6=30 $ cases
Total number of cases $=6+12+18+24+ 30=90$