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Problems Problem

Create 4 Digit Room Codes

A venue uses 6 available symbols to generate 4 character room codes. How many codes are possible if symbols can repeat?

Decision guide

Why this formula fits

This is permutation with repetition because the code positions are ordered and every position can reuse any symbol.

Does order matter? Order matters because 1234 and 4321 are different room codes.

Is repetition allowed? Repetition is allowed, so the same symbol can appear in multiple positions.

Worked solution

6 choices for 4 ordered positions gives 1,296.

  1. Inputs: n = 6, r = 4
  2. Formula: n^r
  3. Substitute: 6^4
  4. Steps: multiply 6 by itself 4 times
  5. Result: 6 choices for 4 ordered positions gives 1,296.

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This is permutation with repetition because the code positions are ordered and every position can reuse any symbol.

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