What is (52!)/((52-5)!5!) ?

The solution to (52!)/((52-5)!5!) is 2598960

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simplify (52!)/((52-5)!5!)

simplify

\frac{52 !}{( 52 - 5 ) ! 5 !}

2598960

Solution steps

\frac{52 !}{( 52 - 5 ) ! \cdot 5 !}

Subtract the numbers:

52 - 5 = 47

= \frac{52 !}{47 ! \cdot 5 !}

Cancel the factorials:

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

\frac{52 !}{47 !} = 52 \cdot 51 \cdot 50 \cdot 49 \cdot 48

= \frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48}{5 !}

\frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48}{5 !} = 2598960

= 2598960

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