Factorials are unnecessary

Algebra Level 1

110×29×38××101,1!×2!×3!××10! 1^{10}\times 2^9\times 3^8\times \cdots \times 10^{1} , \qquad 1!\times2!\times3!\times \cdots \times10! Which of the numbers above is larger?

Details and Assumptions:

  • n!=1×2×3××nn! = 1\times2\times3\times\cdots \times n.
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