化简 (10!)/(7!(10-7)!)

解答

化简

\frac{10 !}{7 ! ( 10 - 7 ) !}

120

求解步骤

\frac{10 !}{7 ! ( 10 - 7 ) !}

数字相减:

10 - 7 = 3

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

消去因子:

\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

e x p an d (x + 2) (x^{2} - 7 x + 4)

\frac{1}{3} \times (\frac{5}{3} + \frac{2}{5})

e x p an d (x + 9) (4 x^{2} + 5 x + 6)

\frac{345}{180}

s im pl i f y (3 m n^{2})^{4}