CAT 2024 Slot 3 QA Q14 Permutations & Probability

Question 14 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

The number of all positive integers up to 500 with non-repeating digits is

TITA: type in the answer. There are no options and no negative marking.

Answer: 378 Permutations & Probability TITA

Solution

  1. 1-digit: 9. 2-digit: \(9 \times 9 = 81\).
  2. 3-digit up to 499: first digit 1-4 (4 ways), then \(9 \times 8\): \(288\). 500 repeats a digit.
  3. Total \(= 9 + 81 + 288 = 378\).

Same concept in other years

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

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