化简 (14!)/((14-4)!4!)

解答

化简

\frac{14 !}{( 14 - 4 ) ! 4 !}

1001

求解步骤

\frac{14 !}{( 14 - 4 ) ! \cdot 4 !}

数字相减:

14 - 4 = 10

= \frac{14 !}{10 ! \cdot 4 !}

消去因子:

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

\frac{14 !}{10 !} = 14 \cdot 13 \cdot 12 \cdot 11

= \frac{14 \cdot 13 \cdot 12 \cdot 11}{4 !}

\frac{14 \cdot 13 \cdot 12 \cdot 11}{4 !} = 1001

= 1001

\frac{x ^{2} + 2 x - 24}{x + 2} < 0

2 y^{2} = 100

5 - 3 x \leq - 16

- 4 (n + 3) < - 24

(x - 7) (3 x + 5) = 0