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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations

A company at Pune assigns each employee a code made of 2 distinct letters chosen from A, B, C, D, E followed by 2 digits chosen from 1 to 9, where digits may repeat. How many codes are possible if the letters must be in alphabetical order (the earlier letter first)?

There are 810 codes. Alphabetical order means only the choice of two letters matters, giving 5C2 = 10 pairs. The two digits each have 9 options with repetition, giving 81. Multiplying gives 10 × 81 = 810.

  1. A810Correct
  2. B1620
  3. C2025
  4. D1000

Explanation

Letter pairs in fixed alphabetical order = 5C2 = 10. Digits with repetition allowed = 9 × 9 = 81. Total = 10 × 81 = 810. The value 1620 counts both letter orders (5 × 4 × 81), which the alphabetical condition rules out.

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