CAT 2021 Slot 3 QA Q4 Permutations & Probability

Question 4 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

A four-digit number is formed by using only the digits 1, 2 and 3 such that both 2 and 3 appear at least once. The number of all such four-digit numbers is

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

Answer: 50 Permutations & Probability TITA

Solution

  1. All 4-digit strings from \(\{1,2,3\}\): \(3^4 = 81\).
  2. Remove those without a 2 (\(2^4 = 16\)) and those without a 3 (\(16\)); add back those with neither (only 1111): \(1\).
  3. \(81 - 16 - 16 + 1 = 50\).

Same concept in other years

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