The number of ways in which 3 boys and 2 girls can be arranged in a queue, given that the 2 girls have to be next to each other, is
12
24
48
120
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2018
We have 3 boys (B) and 2 girls (G). The constraint is that the 2 girls must be next to each other. We can treat the 2 girls as a single combined unit. Now we have 3 boys and this one ‘girl unit’, totaling 4 items to arrange in a queue: B, B, B, (GG). The number of ways to arrange these 4 distinct items (treating the boys as distinct for now, although the problem doesn’t specify, in permutations, items are usually treated as distinct unless stated otherwise) is 4! = 24. However, within the ‘girl unit’ (GG), the two girls can swap positions (G1G2 or G2G1). There are 2! = 2 ways to arrange the 2 girls within their unit. The total number of ways to arrange the 3 boys and 2 girls with the girls together is the product of the number of ways to arrange the 4 items and the number of ways to arrange the girls within their unit. Total ways = 4! * 2! = 24 * 2 = 48.
To solve permutation problems with a constraint that a group of items must stay together, treat the constrained group as a single unit. Calculate the permutations of the units, and then multiply by the permutations within the constrained unit.