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26. A five-digit number divisible by 3 is to be formed using
numerical 0, 1, 2, 3, 4 and 5 without repetition. The
total number of ways this can be done is:
(1) 122 (2) 210
(3) 216 (4) 217
Answers (1)
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For a number to be divisible by 3 , the sum of digits has to be a multiple of 3
let us see the cases when the sum of digits is a multiple of 3
(a) When the digits are 1 ,2 , 3 , 4 , 5
(b) When the digits are 0,1,2,4,5
Total number of numbers formed in the first case = 5! = 120
Total number of numbers formed in second case = 5! - 4 ! = 96
Total number of 5 digit numbers that can be formed using 0,1,2,3,4 and 5 without repetition such that they are divisible by 3 are 120 + 96 = 216