Permutation and CombinationMedium
Question
A five digits number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is
Options
A.216
B.240
C.600
D.3125
Solution
Since, a five digits number is formed using the digits {0, 1, 2, 3, 4 and 5} divisible by 3 ie, only possible when sum of the digits is multiple of three.
Case I : Using disits 0, 1, 2, 4, 5
Number of ways = 4 × 4 × 3 × 2 × 1 = 96
Case II : Using digitd 1, 2, 3, 4, 5,
Number of ways = 5 × 4 × 3 × 2 × 1 = 120
∴ Total numberd = 120 + 96 = 216
Case I : Using disits 0, 1, 2, 4, 5
Number of ways = 4 × 4 × 3 × 2 × 1 = 96
Case II : Using digitd 1, 2, 3, 4, 5,
Number of ways = 5 × 4 × 3 × 2 × 1 = 120
∴ Total numberd = 120 + 96 = 216
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