How many 4-digit numbers, that are divisible by 3, can be formed, using the digits 0, 1, 2, 3 and 4 if no digit is to occur more than once in each number?
Explanation:
For a number to be divisible by 3, the sum of the digits should be divisible by 3.
∴ We need to select 4 numbers whose sum is divisible by 3.
We know 0 + 1 + 2 + 3 + 4 = 10,
Hence, excluding 1 or 4 will give the sum 9 or 6 (divisible by 3)
Case 1: 4 digits are 0, 2, 3 and 4 Number of 4-digit numbers = 3 × 3! = 18.
Case 2: 4 digits are 0, 1, 2 and 3 Number of 4-digit numbers = 3 × 3! = 18.
∴ Total number of numbers = 18 + 18 = 36.
Hence, 36.
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