What is (14!)/(5!(14-5)!) ?

The solution to (14!)/(5!(14-5)!) is 2002

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simplify (14!)/(5!(14-5)!)

simplify

\frac{14 !}{5 ! ( 14 - 5 ) !}

2002

Solution steps

\frac{14 !}{5 ! ( 14 - 5 ) !}

Subtract the numbers:

14 - 5 = 9

= \frac{14 !}{5 ! \cdot 9 !}

Cancel the factorials:

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

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

= \frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{5 !}

\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10}{5 !} = 2002

= 2002

\frac{1}{7} \times 7

2 50 z^{7}

\frac{- 5}{12}