What is (20!)/(10!*(20-10)!) ?

The solution to (20!)/(10!*(20-10)!) is 184756

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simplify (20!)/(10!*(20-10)!)

simplify

\frac{20 !}{10 ! \cdot ( 20 - 10 ) !}

184756

Solution steps

\frac{20 !}{10 ! ( 20 - 10 ) !}

Subtract the numbers:

20 - 10 = 10

= \frac{20 !}{10 ! \cdot 10 !}

Cancel the factorials:

\frac{n !}{( n - m ) !} = n \cdot (n - 1) \dots (n - m + 1), n > m

\frac{20 !}{10 !} = 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11

= \frac{20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{10 !}

\frac{20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{10 !} = 184756

= 184756

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