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Part BCSIR NET December 2024divide-by-the-factorial-of-the-leftover

Divide by the factorial of the leftover

What is the number of injective functions from {1, 2, …, 7} to {1, 2, …, 10}?

  1. A.10710^{7}
  2. B.10!/7!
  3. C.10!/3!✓ Correct
  4. D.7107^{10}

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

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50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Aₙ is simple for every n ≥ 3

More on this topic

The chapter behind this: Permutation groups — cycle type, sign and conjugacy — free to read

From Groups › Permutation groups: cycles, sign, conjugacy in S_n and A_n

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