Question

表达式的值是多少？ $\dfrac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1+2+3+4+5+6+7+8}?$

What is the value of the expression $\dfrac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1+2+3+4+5+6+7+8}?$

$1020$

$1120$

$1220$

$2240$

$3360$

知识点：阶乘

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分母为 $1+2+\cdots+8=36=2\cdot3\cdot6$ 。因此 $4\cdot5\cdot7\cdot8=1120$ 。

所以正确答案是 B。

The denominator is $1+2+\cdots+8=36=2\cdot3\cdot6.$ Canceling those three factors from the numerator leaves $4\cdot5\cdot7\cdot8=1120.$

Thus, B is the correct answer.