UPSC Prelims 2023 · CSAT
Question 19: Basic Numeracy
How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions ?
AnswerUPSC’s answer is (c).
Odd positions 1, 3, 5, 7 must hold the odd digits 1, 1, 3, 3, and even positions 2, 4, 6, 8 the even digits 2, 2, 4, 4. Each group can be arranged in 4!/(2! x 2!) = 6 ways. The two choices are independent, so 6 x 6 = 36 numbers.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Wrong: undercounts; 6 x 6 is 36.
- (b) Wrong: undercounts; 6 x 6 is 36.
- (c) Right: 6 arrangements of odd digits x 6 of even digits = 36.
- (d) Wrong: overcounts; where odd and even digits go is fixed, only the order within each group varies.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.