A five digit number divisible by 3 has to be formed using the numerals 0,1,2,3,4,5 .Find the total number of ways in which this can be done.

Dear Darshita

If a number is divisible by 3, the sum of its digits is divisible by 3. We need to choose five digits from {0,1,2,3,4,5} which add to a multiple of 3. We could choose:

{1, 2, 3, 4, 5}

or

{0, 1, 2, 4, 5}

If we use the digits {1, 2, 3, 4, 5}, we have 5 choices for the first digit, 4 for the second, etc- 5! = 120 numbers we can make in total.

If we use the digits {0, 1, 2, 4, 5}, we only have 4 choices for the first digit (because it cannot be zero), 4 choices for the second digit, 3 for the third, etc- 4*4! = 96 numbers we can make in total.

120+96 = 216.

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

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