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AMO · 2027 · Grades 8-9 · Self-study SET 25 Question 10

AMO

Question 10

Use the standard factorial definition $n!=n(n-1)\cdots2\cdot1$. Simplify
$$\frac{20!+21!}{2\times19!+4\times19!+16\times19!}.$$
Source clarification: the printed definition is $n!=n\times(n-1)!\times\cdots\times2\times1$, with an extra factorial sign after $(n-1)$. We use the standard definition stated above.