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  • 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 A. 216

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
A. 216
B. 600
C. 240
D. 3125
[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.]

Answers (1)

The answer is the option (a).

A number is divisible by 3 if the sum of its digit is divisible by 3. So, to form a number of 5-digit which is divisible by 3 we can remove either 0 or 3. If digits 1,2, 3, 4, 5 are used then the 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, 4*4! Ways.

Total numbers = 120+96 =216

Posted by

infoexpert21

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