CAT 2022 Slot 2 QA Q12 Permutations & Probability

Question 12 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is
  1. A
    1440
  2. B
    1200
  3. C
    1420
  4. D
    1480

Answer: (A) 1440 Permutations & Probability MCQ

Solution

  1. 4-digit numbers above 2000: first digit from {2,3,4,5}: \(4\times5\times4\times3=240\).
  2. 5-digit: \(5\times5\times4\times3\times2=600\). 6-digit: \(5\times5!=600\).
  3. Total \(=240+600+600=1440\).

Same concept in other years

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

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