A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is:
Explanation:
The five digit number will either have 0 or it will not have 0.
Case i:
0 is included.
The five digits must be 0, 1, 2, 4, 5 (as the number has to be divisible by 3)
The count of five-digit numbers = 4 × 4 × 3 × 2 × 1 = 96
Case ii:
0 is excluded.
In this case, the five digits should be 1, 2, 3, 4 and 5.
Number of five digit numbers = 5 × 4 × 3 × 2 × 1 = 120
∴ Required count = 120 + 96 = 216
Hence, option (d).
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