If 2 boys and 2 girls are to be arranged in a row so that the girls are not next to each other, how many possible arrangements are there?
- (a) 3
- (b) 6
- (c) 12 ✓ UPSC's answer
- (d) 24
Why the answer is (c)
• Arrange the 2 boys first: 2 ways. This creates 3 gaps (before, between, after).
• Put the 2 girls into 2 different gaps so they are not next to each other: 3 × 2 = 6 ways (choosing and ordering the gaps).
• Total = 2 × 6 = 12, option (c).
• Check: of the 24 arrangements of 4 people, 12 have the girls together (3 positions for the pair × 2 × 2), leaving 12.
Why the other options are wrong
- (a) 3
- 3 is the number of ways to choose the spaces for the girls, not the total arrangements including the boys' permutations.
- (b) 6
- 6 is the number of ways to arrange the girls in the spaces or the total permutations of 3 items, ignoring the boys' distinct arrangements.
- (d) 24
- 24 is the total number of unrestricted arrangements of 4 distinct people (4!), which includes cases where the girls are adjacent.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.