Maths Olympiad Prep

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Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

Two brothers and three sisters form a single line for a photograph. The two boys refuse to stand next to each other. How many different line-ups are possible?

(A) 2424 (B) 3636 (C) 6060 (D) 7272 (E) 120120

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.