What is (5!8!)/(2!9!) ?

The solution to (5!8!)/(2!9!) is 20/3

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simplify (5!8!)/(2!9!)

simplify

\frac{5 ! 8 !}{2 ! 9 !}

\frac{20}{3}

Decimal Notation

6.66666 \dots

Solution steps

\frac{5 ! \cdot 8 !}{2 ! \cdot 9 !}

Cancel the factorials:

\frac{n !}{( n + m ) !} = \frac{1}{( n + 1 ) \cdot ( n + 2 ) \dots ( n + m )}

\frac{8 !}{9 !} = \frac{1}{9}

= \frac{5 !}{2 ! \cdot 9}

Cancel the factorials:

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

\frac{5 !}{2 !} = 5 \cdot 4 \cdot 3

= \frac{5 \cdot 4 \cdot 3}{9}

Cancel

\frac{5 \cdot 4 \cdot 3}{9} : \frac{5 \cdot 4}{3}

= \frac{5 \cdot 4}{3}

Multiply the numbers:

5 \cdot 4 = 20

= \frac{20}{3}

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