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Asked • 03/19/19

Combinations [fundemental counting principal]?

> How many 3-digit integers can be chosen such that none of the digits > appear more than twice and none of the digits equal zero? I have approached the following problem like this. 1. We know that zero is not included so we can choose anything from 1-9 which gives us 9 options. 2. We have to select a 3 digit integer therefore we have _ _ _ 3 different stages and we can use the fundamental counting principle. 3. We have 1 constraint that is that none of the digits can be repeated more then 2 times. So i did 9 * 9 * 9 and got 729. This is wrong though because i have not taken into account the constrain of not having 3 repeated digits. Can anyone explain how i would remove the repeated digits from this?

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