What is (4!8!)/(6!7!) ?

The solution to (4!8!)/(6!7!) is 4/15

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simplify (4!8!)/(6!7!)

simplify

\frac{4 ! 8 !}{6 ! 7 !}

\frac{4}{15}

Decimal Notation

0.26666 \dots

Solution steps

\frac{4 ! \cdot 8 !}{6 ! \cdot 7 !}

Cancel the factorials:

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

\frac{8 !}{7 !} = 8

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

Cancel the factorials:

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

\frac{4 !}{6 !} = \frac{1}{5 \cdot 6}

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

Cancel

\frac{8}{5 \cdot 6} : \frac{4}{5 \cdot 3}

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

Multiply the numbers:

5 \cdot 3 = 15

= \frac{4}{15}

\frac{x + 1}{3} + 2 = 9

(x + 5)^{2} - 7 = 0

2 x + 1 \geq 3 x - 2 (5 x - 4)

(\frac{4}{6})^{5}

- 8 (n - 4) = n - 40