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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

Combinatorics

Counting

Source of the Problem

Answer

AMC 8 2020 Problem 7

15

Hint 1

Hint 2

Hint 3

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.

Try 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.

- 9
- 10
- 15
- 21
- 28

Combinatorics

Counting

Source of the Problem

Answer

AMC 8 2020 Problem 7

15

Hint 1

Hint 2

Hint 3

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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