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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

\frac{5}{14}

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}

x^{2} - 20 x - 44 = 0

\frac{18 x y}{30 x ^{6} y ^{7}}

(\frac{9}{4})^{2}

(x)^{- \frac{1}{2}}

\frac{12}{3} > x