Problems Problem

Choose 5 Finalists From 12 Applicants

An awards panel must choose 5 finalists from 12 applicants. How many different finalist groups are possible if no applicant can be selected twice?

Decision guide

Why this formula fits

This is a plain combination problem because the panel is forming one group of finalists, order does not matter, and each applicant can be selected at most once.

Does order matter? Order does not matter. A finalist group with the same 5 applicants is the same group no matter what order you list their names.

Is repetition allowed? Repetition is not allowed because the same applicant cannot fill more than one finalist spot.

Worked solution

12 choose 5 without repeats is 792.

  1. Inputs: n = 12, r = 5
  2. Formula: C(n, r) = n! / (r!(n-r)!)
  3. Substitute: C(12, 5) = 12! / (5!(12-5)!)
  4. Steps: 479,001,600 / (120 x 5,040)
  5. Result: 12 choose 5 without repeats is 792.

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This is a plain combination problem because the panel is forming one group of finalists, order does not matter, and each applicant can be selected at most once.

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