What is (20!)/(5!(20-5)!) ?

The solution to (20!)/(5!(20-5)!) is 15504

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simplify (20!)/(5!(20-5)!)

simplify

\frac{20 !}{5 ! ( 20 - 5 ) !}

15504

Solution steps

\frac{20 !}{5 ! ( 20 - 5 ) !}

Subtract the numbers:

20 - 5 = 15

= \frac{20 !}{5 ! \cdot 15 !}

Cancel the factorials:

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

\frac{20 !}{15 !} = 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16

= \frac{20 \cdot 19 \cdot 18 \cdot 17 \cdot 16}{5 !}

\frac{20 \cdot 19 \cdot 18 \cdot 17 \cdot 16}{5 !} = 15504

= 15504

43 + 4 i

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