Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?
- (a) 3
- (b) 6 ✓ UPSC's answer
- (c) 9
- (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.