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Explore the Back-StoryTry this beautiful Problem based on combinatorics from AMC 8 2020.

How many integers between 2020 and 2400 have four distinct digits arranged in increasing order? (For example, 2347 is one integer.

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Combinatorics

Counting

AMC 8 2020 Problem 7

15

The second digit can't be 1 or 2, since the digit need to be increasing and distinct , and the second digit can't be 4 also since the number need to be less than 2400, so its 3

now we need to choose the last two digit from the set $\{4,5,6,7,8,9\}$

now we can do it in $6C2= 15$ ways. now in only one way we can order so there are 15 numbers.

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