UPSC Prelims 2009 · General Studies
Question 98: Basic Numeracy
How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order?
AnswerThe answer is (d).
Any three different digits from 1-9 can be written in only one strictly ascending order, so the count is the number of ways to choose 3 digits from 9: 9C3 = (9 x 8 x 7) / (3 x 2 x 1) = 84. For example, 2, 5 and 8 give only 258.
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.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
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) 80 is not the number of 3-digit selections.
- (b) 81 is 9 x 9, which ignores ordering.
- (c) 83 is not 9C3.
- (d) Right: 9C3 = 84.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2009, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.