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?
Answer & explanation
Answer: (c) 12
There are 4! = 24 arrangements in all. Treating the two girls as one block gives 3! × 2 = 12 arrangements in which they sit together, so 24 − 12 = 12 keep the girls apart.
- All arrangements of 4 different children: 4! = 24.
- Girls together: treat them as one unit → 3 units → 3! = 6, and the girls can swap within the unit → 6 × 2 = 12.
- Girls not together: 24 − 12 = 12.
- Check (gap method): arrange the boys in 2! = 2 ways, leaving 3 gaps; place the two girls in 2 of the gaps in 3 × 2 = 6 ways; total 2 × 6 = 12.
Remember · 'Not together' = total − together; or seat the others first and put the separated people in the gaps.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·