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A five digit number divisible by 3 has to be formed using the numerals 0,1,2,3,4 and 5 without repetition. What is the total number of ways in which this can be done? |
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Answer» A five digit number is divisible by 3 if the sum of the digits constituting the number is divisible by 3. On mental summing up we see that 1,2,3,4,5 is a group and 0,1,2,4,5 another group. First group can form 5! =120 numbers which are divisible by 3 And effective 5 digit number formed by 2nd group will be 5!-4!=96, where 4! is the number of numbers which start with zero. So neglected. Hence required number of 5 digit numbers divisible by 3 is (120+96)=216 |
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