AMC8 1990

AMC8 1990 · Q12

AMC8 1990 · Q12. It mainly tests Basic counting (rules of product/sum), Permutations.

There are twenty-four 4-digit whole numbers that use each of the four digits 2, 4, 5, and 7 exactly once. Listed in numerical order from smallest to largest, the number in the 17th position in the list is

有二十四个4位数的整数，它们恰好各使用一次数字2、4、5和7。从最小到最大按数值顺序排列，列表中第17个位置的数是

(A) 4527 4527

(B) 5724 5724

(D) 7245 7245

(E) 7542 7542

Answer

Correct choice: (B)

正确答案：（B）

Solution

1/4 of 24=6 begin with each digit. 1-6:2xxx,7-12:4xxx,13-18:5xxx. Fifth with 5: 5247,5274,5427,5472,5724.

24的1/4=6，以每个数字开头各有6个。1-6:2xxx，7-12:4xxx，13-18:5xxx。以5开头的第五个：5247,5274,5427,5472,5724。

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