What is (14!)/((14-6)!6!) ?

The solution to (14!)/((14-6)!6!) is 3003

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simplify (14!)/((14-6)!6!)

simplify

\frac{14 !}{( 14 - 6 ) ! 6 !}

3003

Solution steps

\frac{14 !}{( 14 - 6 ) ! \cdot 6 !}

Subtract the numbers:

14 - 6 = 8

= \frac{14 !}{8 ! \cdot 6 !}

Cancel the factorials:

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

\frac{14 !}{8 !} = 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9

= \frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9}{6 !}

\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9}{6 !} = 3003

= 3003

(1 + \frac{2}{n})^{n}

x^{2} - 7 = 6 x

6 x^{2} - x < 2

4100