What is (6!7!)/(4!9!) ?

The solution to (6!7!)/(4!9!) is 5/12

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simplify (6!7!)/(4!9!)

simplify

\frac{6 ! 7 !}{4 ! 9 !}

\frac{5}{12}

Solution steps

\frac{6 ! \cdot 7 !}{4 ! \cdot 9 !}

Cancel the factorials:

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

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

= \frac{6 \cdot 5 \cdot 7 !}{9 !}

Cancel the factorials:

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

\frac{7 !}{9 !} = \frac{1}{8 \cdot 9}

= \frac{6 \cdot 5}{8 \cdot 9}

Cancel

\frac{6 \cdot 5}{8 \cdot 9} : \frac{5}{4 \cdot 3}

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

Multiply the numbers:

4 \cdot 3 = 12

= \frac{5}{12}

3 x - x + 2 > 4 - 6

lo g_{4} (3) = n - 2

20 lo g_{10} (10)

\frac{10 - x}{4 x - 7} < 5