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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
  • a)
    216         
  • b)
    240                 
  • c)
    600                 
  • d)
    3125
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A five digit number divisible by 3 is to be formed using the numerals ...
If a number is divisible by 3, the sum of the digits in it must be a multiple of 3.
The sum of the given six numerals is 0 + 1 + 2 + 3 + 4 + 5 = 15.
So to make a five digit number divisible by 3 we can either exclude 0 or 3.
If 0 is left out, then 5! = 120 number of ways are possible.
If 3 is left out, then the number of ways of making a five digit number is 4 × 4! = 96, because 0 cannot be placed in the first place from left, as it will give a number of four digits.
Thus, the required number of ways = 120 + 96 = 216.  
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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 isa)216 b)240 c)600 d)3125Correct answer is option 'A'. Can you explain this answer?
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