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UKMT Intermediate Mathematical Challenge, 2025

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Lottie wants to colour two rows and two columns of the $4 \times 7$ grid shown so that the coloured rows do not touch and also the coloured columns do not touch. In how many ways can she do this?

(A) $45$ (B) $42$ (C) $40$ (D) $35$ (E) $30$

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