Mary typed a six digit number

Dear Math Experts, I am an eighth grade student and have been stumped with this problem. Please help!

Thanks,
Pillar

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?

Hi Pillar,

The four digits that you have leave five places for the missing digits

_2_0_0_2_ 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.

Penny

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