What is (10!)/(3!(10-3)!) ?

The solution to (10!)/(3!(10-3)!) is 120

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simplify (10!)/(3!(10-3)!)

simplify

\frac{10 !}{3 ! ( 10 - 3 ) !}

120

Solution steps

\frac{10 !}{3 ! ( 10 - 3 ) !}

Subtract the numbers:

10 - 3 = 7

= \frac{10 !}{3 ! \cdot 7 !}

Cancel the factorials:

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

\frac{10 !}{7 !} = 10 \cdot 9 \cdot 8

= \frac{10 \cdot 9 \cdot 8}{3 !}

\frac{10 \cdot 9 \cdot 8}{3 !} = 120

= 120

4 x^{2} - 9

\frac{7 x + 2}{3 x - 1} \leq 4

\frac{- 2 ( x - 1 )}{3} = \frac{2 - x}{4}

22 x + 35 = 12 x + 85

18 x^{4} + 87 x^{3} + 3 x^{2} - 108 x