Set A has 4 elements and the set B has 6 elements, then the number of injective mappings that can be defined from A to B is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 360
An injective (one-one) mapping sends different elements of A to different elements of B. Let \(A = \{a_1, a_2, a_3, a_4\}\). Choosing the images one by one:
\(a_1: 6 \text{ choices},\quad a_2: 5,\quad a_3: 4,\quad a_4: 3\)
\(\text{Number of injective maps} = 6 \times 5 \times 4 \times 3 = 360\)
This is \(^{6}P_{4} = \frac{6!}{2!} = 360\).
Why the other options are incorrect
Option (2) 15 — Incorrect. This is \(^{6}C_{4}\), which only chooses the 4 images and ignores which element goes to which.
Option (3) 24 — Incorrect. This is 4!, the number of one-one maps from A onto a fixed set of 4 elements.
Option (4) 1296 — Incorrect. This is \(6^4\), the number of all mappings from A to B, one-one or not.