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UKMT Senior Mathematical Challenge, 2021

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

Alison has a set of ten fridge magnets showing the integers from $0$ to $9$ inclusive. In how many different ways can she split the set into five pairs so that the sum of each pair is a multiple of $5$ ?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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