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.
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.
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.
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.
