Question

If the set $A$ contains $5$ elements and the set $B$ contains $6$ elements, then the number of one-one and onto mappings from $A$ to $B$ is

• A. $720$
• B. $120$
• C. $0$
• D. none of these

Answer 1

Answer: (C)

As A contains $5$ elements.
$\therefore$ For any one-one onto mapping $f$ : $A\to B$, $f(A)$ also contains $5$ elements but $B$ contains $6$ elements.
$\therefore f(A)\ne B$.
So, no one-one mapping from $A$ to $B$ can be onto.