How Cheenta works to ensure student success?
Explore the Back-Story

AMC 8 2020 Problem 7 | Counting Problem

Join Trial or Access Free Resources

Try this beautiful Problem based on combinatorics from AMC 8 2020.

Counting Problem - AMC 8 2020 Problem 7

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

  • 9
  • 10
  • 15
  • 21
  • 28

Key Concepts



Suggested Book | Source | Answer

AMC 8 2020 Problem 7


Try with Hints

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.

Subscribe to Cheenta at Youtube

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
Math Olympiad Program