In how many different ways can three students be assigned to four chartered accountants, if each chartered accountant can take at most one student?

Introduction / Context:
This question checks understanding of permutations and the idea of assigning people to distinct positions. We have fewer students than chartered accountants, and each accountant can supervise at most one student. We must count the number of possible assignments where all three students are placed with different accountants.

Given Data / Assumptions:

There are 3 distinct students.

There are 4 distinct chartered accountants.

Each accountant can supervise at most one student.

Each student must be assigned to exactly one accountant.

Concept / Approach:
We are assigning 3 distinct students to 4 distinct “positions” (the accountants), with no two students going to the same accountant. This is a permutation or injective mapping from 3 students into 4 accountants. The number of such assignments is 4P3, which can be computed as 4 * 3 * 2.

Step-by-Step Solution:
Step 1: Choose an accountant for the first student. There are 4 choices.Step 2: After assigning the first student, only 3 accountants remain free for the second student.Step 3: After assigning the second student, only 2 accountants remain free for the third student.Step 4: Total number of assignments = 4 * 3 * 2 = 24.

Verification / Alternative check:
Using permutation notation, the number of ways of assigning 3 students to 4 accountants is 4P3. We know 4P3 = 4! / (4 - 3)! = 4! / 1! = 24. This matches the direct multiplication method, so the answer is confirmed.

Why Other Options Are Wrong:
12 would correspond to 4 * 3, which ignores the arrangements for the third student.
36 does not match any correct permutation formula in this setup and usually comes from random multiplication or adding extra factors incorrectly.
16 may come from thinking that each of the 4 accountants has 2 possible states (assigned or not), which does not model the actual assignment process.

Common Pitfalls:
A frequent mistake is to think in terms of combinations and compute 4C3, which counts only which accountants are used, not which student is attached to whom. Another error is to assume students are identical and ignore ordering, which is not correct here. We must respect that both students and accountants are distinct individuals.

Final Answer:
The number of ways to assign the three students is 24.