Question

If set $A$ has 3 elements and set $B$ has 4 elements, then the number of injective mappings from $A$ to $B$ is

• A. 144
• B. 12
• C. 24
• D. 64

Hint:

Injective mappings are calculated using permutations, not combinations.

Answer 1

The Correct Option is C

Step 1: Understand injective mapping.
An injective (one-to-one) mapping assigns distinct elements of $A$ to distinct elements of $B$.
Step 2: Apply the formula.
Number of injective mappings from a set of $m$ elements to a set of $n$ elements is \[ {}^nP_m \]
Step 3: Substitute values.
Here, $m = 3$ and $n = 4$.
\[ {}^4P_3 = 4 \times 3 \times 2 = 24 \]