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UKMT Senior Mathematical Challenge, 2021

Number theory Difficulty 1.0 Junior Find the answer United Kingdom

The number $840$ can be written as $\frac{p!}{q!}$ , where $p$ and $q$ are positive integers less than $10$ . What is the value of $p + q$ ? Note that, $n! = 1 \times 2 \times 3 \times \cdots \times (n-1) \times n$ .

(A) $8$ (B) $9$ (C) $10$ (D) $12$ (E) $15$

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