Question

The number of functions that can be defined from the set $A=\{a,b,c,d\}$ into the set $B=\{1,2,3\}$ is

• A. $12$
• B. $24$
• C. $64$
• D. $81$
• E. $256$

Answer 1

The correct option is D $81$

Given, $A=\{a,b,c,d\}$ and $B=\{1,2,3\}$

Element $a$ can be have an image in $3$ ways, i.e., $(1,2,$ or $3$).
Similarly $b,c$ and $d$ can have an image in $3$ ways.
Thus total number of ways $=3\times 3\times 3\times 3\times =81$.