CAT 2023 Slot 1 QA Q21 Permutations & Probability

Question 21 of the Quantitative Ability (QA) section, CAT 2023 Slot 1, with CAT's official answer and a worked solution.

The number of all natural numbers up to 1000 with non-repeating digits is
  1. A
    585
  2. B
    504
  3. C
    648
  4. D
    738

Answer: (D) 738 Permutations & Probability MCQ

Solution

  1. 1-digit numbers: 9.
  2. 2-digit with distinct digits: \(9\times9 = 81\).
  3. 3-digit with distinct digits: \(9\times9\times8 = 648\). (1000 has repeated zeros.)
  4. Total \(= 9 + 81 + 648 = 738\).

Same concept in other years

See every question on Counting numbers with distinct digits under conditions.

More Permutations & Probability questions from CAT

All 21 Permutations & Probability questions asked since 2017.