What is (34!)/((34-8)!8!) ?

The solution to (34!)/((34-8)!8!) is 18156204

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simplify (34!)/((34-8)!8!)

simplify

\frac{34 !}{( 34 - 8 ) ! 8 !}

18156204

Solution steps

\frac{34 !}{( 34 - 8 ) ! \cdot 8 !}

Subtract the numbers:

34 - 8 = 26

= \frac{34 !}{26 ! \cdot 8 !}

Cancel the factorials:

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

\frac{34 !}{26 !} = 34 \cdot 33 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28 \cdot 27

= \frac{34 \cdot 33 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28 \cdot 27}{8 !}

\frac{34 \cdot 33 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28 \cdot 27}{8 !} = 18156204

= 18156204

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