How many counting numbers between 100 and 1000 have at least one 2 as a digit?
There are 900 of those counting numbers with no restriction.
Let's find all those that DON'T have a 2 in them
there are 8 possible in the left spot , (no 2 or 0)
but 9 anywhere else
number of counting numbers with NO 2 in them is
8x9x9 = 648
So 900 - 648 or 252 of them have at least one 2 in them.
To find the number of counting numbers between 100 and 1000 that have at least one 2 as a digit, we can use the concept of complementary counting.
Step 1: Count the total number of counting numbers between 100 and 1000, inclusively.
There are 1000 - 100 + 1 = 901 counting numbers between 100 and 1000.
Step 2: Count the number of counting numbers between 100 and 1000 that do not have any 2 as a digit.
If there are no 2's as digits, then we have 9 options (0, 1, 3, 4, 5, 6, 7, 8, 9) for each of the three digits. So, there are 9 * 9 * 9 = 729 counting numbers between 100 and 1000 with no 2 as a digit.
Step 3: Subtract the number of counting numbers with no 2 as a digit from the total number of counting numbers between 100 and 1000.
901 - 729 = 172
Therefore, there are 172 counting numbers between 100 and 1000 that have at least one 2 as a digit.