What is (12!)/((12-6)!6!) ?

The solution to (12!)/((12-6)!6!) is 924

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simplify (12!)/((12-6)!6!)

simplify

\frac{12 !}{( 12 - 6 ) ! 6 !}

924

Solution steps

\frac{12 !}{( 12 - 6 ) ! \cdot 6 !}

Subtract the numbers:

12 - 6 = 6

= \frac{12 !}{6 ! \cdot 6 !}

Cancel the factorials:

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

\frac{12 !}{6 !} = 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7

= \frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{6 !}

\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7}{6 !} = 924

= 924

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