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A factorial ratio that's a factorial

EasyBrainteasers~2m

10!6!=n!\dfrac{10!}{6!} = n! for some positive integer nn. What is nn?

Show hints (2)+
  1. 10!/6!=10⋅9⋅8⋅710!/6! = 10\cdot9\cdot8\cdot7.
  2. That product is 50405040 - which factorial is that?

Answer

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7

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Asked at: Jane Street, SIG

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