What is (5!6!)/(3!8!) ?

The solution to (5!6!)/(3!8!) is 5/14

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simplify (5!6!)/(3!8!)

simplify

\frac{5 ! 6 !}{3 ! 8 !}

\frac{5}{14}

Decimal Notation

0.35714 \dots

Solution steps

\frac{5 ! \cdot 6 !}{3 ! \cdot 8 !}

Cancel the factorials:

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

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

= \frac{5 \cdot 4 \cdot 6 !}{8 !}

Cancel the factorials:

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

\frac{6 !}{8 !} = \frac{1}{7 \cdot 8}

= \frac{5 \cdot 4}{7 \cdot 8}

Cancel

\frac{5 \cdot 4}{7 \cdot 8} : \frac{5}{7 \cdot 2}

= \frac{5}{7 \cdot 2}

Multiply the numbers:

7 \cdot 2 = 14

= \frac{5}{14}

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