We want to find how many integers are between 2020 and 2400 such that a criteria is meet, and the criteria is that the four digits are different and are arranged in increasing order.
We will see that there are 15 of these numbers between 2020 and 2400, so the correct option is C.
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To count the number of digits that meet the given criteria, we first need to analyze how the criteria is.
If the numbers must be in increasing order, then the smallest number that can be in the hundreds place is 3 (the smaller integer larger than 2).
so we have:
23__
The number next to the 3 can be a 4, for example:
234_
And the final number can be any number larger than 4, so we have {5, 6, 7, 8, 9} a total of 5 options.
If instead of a 4, the number next to the 3 is a 5, we have:
235_
And the number next to the five can be any digit larger than 5, so now we have 4 options.
Now, we can't have another number than a 3 in the hundreds place, because if we put a 4 there, we are out of the range, and 3 is the smallest digit that we can use there.
Then we already saw all the possible numbers that we can make, adding the numbers of options that we got above we will get:
5 + 4 + 3 + 2 + 1 = 15
This means that are 15 of these numbers between 2020 and 2400. Then the correct option is C.
If you want to learn more, you can read:
https://brainly.com/question/3730774
