What is (52!)/((52-7)!7!) ?

The solution to (52!)/((52-7)!7!) is 133784560

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simplify (52!)/((52-7)!7!)

simplify

\frac{52 !}{( 52 - 7 ) ! 7 !}

133784560

Solution steps

\frac{52 !}{( 52 - 7 ) ! \cdot 7 !}

Subtract the numbers:

52 - 7 = 45

= \frac{52 !}{45 ! \cdot 7 !}

Cancel the factorials:

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

\frac{52 !}{45 !} = 52 \cdot 51 \cdot 50 \cdot 49 \cdot 48 \cdot 47 \cdot 46

= \frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48 \cdot 47 \cdot 46}{7 !}

\frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48 \cdot 47 \cdot 46}{7 !} = 133784560

= 133784560

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