Choose the correct answer. A five digit number divisible by 3 is … - Vidyadip

MCQ

Choose the correct answer. A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is.
[Hint: 5 digit numbers can be formed using digits 0, 1, 2, 4, 5 or by using digits 1, 2, 3, 4, 5 since sum of digits in these cases is divisible by 3.]

✓
216
B
600
C
240
D
3125

✓

Answer

Correct option: A.

216

We know that a number is divisible by 3 if the sum of its digits is divisible by 3.
Now sum of the given six digits is 15 which is divisible by 3. So to form a number of five-digit which is divisible by 3 we can remove either ‘O’ or ‘3’. If digits 1, 2, 3, 4, 5 are used then number of required numbers = 5!
If digits 0, 1, 2, 4, 5 are used then first place from left can be filled in 4 ways and remaining 4 places can be filled in 4! ways. So in this case required numbers are 4 × 4! ways.
So, total number of numbers = 120 + 96 = 216

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