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Find how many distinct numbers greater than 5000 and divisible by 3 can be formed

from digits 3,4,5,6,and 0, each digit being used at most once in any number.

A number is divisible by 3 if its sum of digits is divisible by 3.

Four-digit numbers

The number begins with 5: .

The other 3 digits can be: .

. . Each has permutations.

Hence, there are: four-digit numbers that begin with 5.

The number begins with 6: .

The other 3 digits can be: .

. . Each has permutations.

Hence, there are: four-digit numbers that begin with 6.

There are: four-digit numbers.

Five-digit numbers

The digits add up to 18, a multiple of 3.

Hence,five-digit number will be divisible by 3.any

There are choices for the first digit.

The other 4 digits can be permuted in ways.

Hence, there are: five-digit numbers.

Therefore, there are : such numbers.