What is (10!)/((10-4)!4!) ?

The solution to (10!)/((10-4)!4!) is 210

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simplify (10!)/((10-4)!4!)

simplify

\frac{10 !}{( 10 - 4 ) ! 4 !}

210

Solution steps

\frac{10 !}{( 10 - 4 ) ! \cdot 4 !}

Subtract the numbers:

10 - 4 = 6

= \frac{10 !}{6 ! \cdot 4 !}

Cancel the factorials:

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

\frac{10 !}{6 !} = 10 \cdot 9 \cdot 8 \cdot 7

= \frac{10 \cdot 9 \cdot 8 \cdot 7}{4 !}

\frac{10 \cdot 9 \cdot 8 \cdot 7}{4 !} = 210

= 210

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