UPSC Prelims 2021 CSAT Paper II · Q66 of 79 Mental Ability medium

Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?

  1. (a) 3
  2. (b) 6 ✓ UPSC's answer
  3. (c) 9
  4. (d) 12

Why the answer is (b)

• The digits available are 2, 2, 3, 3, 3. To form a number greater than 30000, the first digit must be 3.

• After placing 3 in the first position, the remaining digits to arrange are 2, 2, 3, 3.

• The number of distinct permutations of these 4 digits, where 2 appears twice and 3 appears twice, is calculated as 4! / (2! * 2!).

• This simplifies to (24) / (2 * 2) = 24 / 4 = 6.

• Therefore, there are exactly 6 distinct numbers greater than 30000 that can be formed.

Why the other options are wrong

(a) 3
Option (a) is incorrect because it undercounts the permutations; the correct calculation yields 6, not 3.
(c) 9
Option (c) is incorrect because it overcounts the permutations; the correct calculation yields 6, not 9.
(d) 12
Option (d) is incorrect because it overcounts the permutations; the correct calculation yields 6, not 12.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

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