How many 4-digit numbers can be formed which are multiples of 3, if repetition of digits is not allowed?
Explanation:
For the number to be divisible by 3, the sum of the digits should be divisible by 3.
Here sum of 5 digits is 2 + 3 + 4 + 7 + 8 = 24.
We need to select 4 numbers (or leave out 1 number) such that sum is divisible by 3.
The only way sum would be divisible by 3 is when we select 2, 4, 7 and 8.
∴ We have to form a 4-digit number using 2, 4, 7 and 8 without repetition.
⇒ Number of ways = 4! = 24.
Hence, 24.
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