Question

Set $A$ consists of $4$ distinct elements $\&$ the set $B$ consists of $5$ distinct elements. Number of mapping defined from $A$ $\to$ $B$ which are not injective is...

• A. $600$
• B. $550$
• C. $505$
• D. none

Answer 1

The correct option is B $550$

Each element of A has $5$ choices thus total ways $=5\times 5\times 5\times 5=625$

If a map is injective then $1$st element of A has $5$ choices, $2$nd element has $(5-1)=4$ choices, $3$rd has $(4-1)=3$ choices & $4$th has $(3-1)=2$ choices.

Thus total injective map$=5\times 4\times 3\times 2=120$

Thus non injective maps$=625-120=505$.