What is (8!7!)/(9!5!) ?

The solution to (8!7!)/(9!5!) is 14/3

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simplify (8!7!)/(9!5!)

simplify

\frac{8 ! 7 !}{9 ! 5 !}

\frac{14}{3}

Decimal Notation

4.66666 \dots

Solution steps

\frac{8 ! \cdot 7 !}{9 ! \cdot 5 !}

Cancel the factorials:

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

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

= \frac{7 !}{9 \cdot 5 !}

Cancel the factorials:

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

\frac{7 !}{5 !} = 7 \cdot 6

= \frac{7 \cdot 6}{9}

Cancel

\frac{7 \cdot 6}{9} : \frac{7 \cdot 2}{3}

= \frac{7 \cdot 2}{3}

Multiply the numbers:

7 \cdot 2 = 14

= \frac{14}{3}

∣ x ∣ = - 14

6 n^{2} = 9 n

4 = x + 5 - 6 x

x^{2} + 6 x + 144 = 0

5 x^{2} - 27 x y + 10 y^{2}