Dear Math Experts,
I am an eighth grade student and have been stumped with this problem.
Six Digit Number
Mary typed a six digit number, but the two 1's did not show. What appeared instead was 2002. How many different six-digit numbers could she have typed?
The four digits that you have leave five places for the missing digits
If the two missing 1's are not adjacent then they can be in any 2 of the 5 available places. This can happen in 5-choose-2 ways, which is 10 ways. If the two missing 1's are adjacent then their position can be in any of the five available spaces, which is 5 more ways.
Hence, in total, there are 10 + 5 = 15 possible six-digit numbers that Mary typed.