Answer :
Final answer:
There are 600 possible five digit numbers using the numbers 0-5 without repetition that are divisible by 3. This is determined using permutations and the divisibility rule of 3.
Explanation:
This is a question of permutations and divisibility. A five digit number that is divisible by 3 using the numbers 0,1,2,3,4,5 without repetitions is to be formed. Given the restriction of no repetitions, the first place can have any of 5 numbers (1-5), second place 5 remaining choices (since 0 can be used), then 4, then 3, and finally 2 choices left for the last spot. So in total, that's a permutation of 5 x 5 x 4 x 3 x 2 = 600 possibilities. The divisibility rule of 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3. Since numbers 0, 1, 2, 3, 4, 5 adds to 15 which is divisible by 3, all 600 possibilities would be divisible by 3. Therefore, the answer to the question is 600.
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