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Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers is
  • a)
    312
  • b)
    3125
  • c)
    120
  • d)
    216
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Five digit number divisible by 3 is formed using the digits 0, 1 , 2, ...
A number is divisible by 3 if and only if the sum of its digits are divisible by 3
Notice that 1 + 2 + 3 + 4 + 5 = 15, which is divisible by 3
The only other way we can have a sum of 5 digits divisible by 3 is to replace the 3 by the 0 making the sum 3 less:
1 + 2 + 0 + 4 + 5 = 12, which is divisible by 3
No other choice of 5 digits can have a sum divisible by 3, because there is no other way to make the sum 12 or 15, and we certainly can't have a sum of 9 or 18
So the number of 5-digit numbers that can be formed from the digits {1,2,3,4,5} is

Number of ways = 1 x 2 x 3 x 4 x 5 = 120
And the number of 5-digit numbers that can be formed from the digits {1, 2, 0, 4, 5} is figured this way

Number of ways = 1 x 2 x 3 x 4 x 4 = 96
Total Number of ways = 120 + 96 = 216
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Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers isa)312b)3125c)120d)216Correct answer is option 'D'. Can you explain this answer?
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