What is (5!7!)/(3!6!) ?

The solution to (5!7!)/(3!6!) is 140

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simplify (5!7!)/(3!6!)

simplify

\frac{5 ! 7 !}{3 ! 6 !}

140

Solution steps

\frac{5 ! \cdot 7 !}{3 ! \cdot 6 !}

Cancel the factorials:

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

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

= \frac{7 !}{3 ! \cdot 6}

Cancel the factorials:

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

\frac{7 !}{3 !} = 7 \cdot 6 \cdot 5 \cdot 4

= \frac{7 \cdot 6 \cdot 5 \cdot 4}{6}

Cancel the common factor:

6

= 7 \cdot 5 \cdot 4

Multiply the numbers:

7 \cdot 5 \cdot 4 = 140

= 140

(x + 1)^{2} = 4

- \frac{5}{9} y + 6 = 4 - \frac{4}{3} y

5 x^{2} + 2 x + 3 \leq 0

3 x + 6 = 21

3 x^{2} + 2 x - 16