¶ 2020 AMC8 Problem 7
Problem:
How many integers between and have four distinct digits arranged in increasing order? (For example, is one integer.)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The digits are in increasing order so the first digit must be , the second digit must be , and the third digit must be . The possible integers are listed below.
The total is integers.
The first digit must be , the second digit must be , and the remaining two digits must be chosen from among the six digits . There are pairs of those digits and only one possible order for each pair, so there are such integers.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions