I don't know a formula that would give the final answer. However, I recommend first finding out which (or, rather, how many) subsets of three cards are allowed and then using the standard formula for the number of permutations of each subset.
There are four cards. In each there's one of these numbers written: 1, 2, 3, 4 (every used once). Three digit numbers are made with the cards, putting the cars variously. How many three digit numbers can be made up, that can be divided by three?
My first question: is there a formula that'll help me to calculate this, or do I need to write all the possible three digit numbers and choose ones that can be divided by 3?
I don't know a formula that would give the final answer. However, I recommend first finding out which (or, rather, how many) subsets of three cards are allowed and then using the standard formula for the number of permutations of each subset.
By "allowed subsets" in post #2 I meant those sets of three cards (or digits) that form numbers divisible by 3. For example, {2, 3, 4} is allowed because any number built from these thee digits is divisible by 3, but {1, 2, 4} is not allowed because numbers built from these digits are not divisible by 3.
You need to answer two questions: how many numbers can be built from a given subset of three digits, and how many 3-element subsets of digits are allowed.