A) 216
B) 240
C) 600
D) 3125
Correct Answer: A
Solution :
We know that a five digit number is divisible by 3, if and only if sum of its digits (= 15) is divisible by 3, therefore we should not use 0 or 3 while forming the five digit numbers. Now, (i) In case we do not use 0 the five digit number can be formed (from the digit 1, 2, 3, 4, 5) in \[^{5}{{P}_{5}}\]ways. (ii) In case we do not use 3, the five digit number can be formed (from the digit 0, 1, 2, 4, 5) in \[\ 6\ !\ -5\ !\ \times 2=480\] ways. \[\therefore \] The total number of such 5 digit number \[={{\,}^{5}}{{P}_{5}}+{{(}^{5}}{{P}_{5}}{{-}^{4}}{{P}_{4}})=120+96=216\].
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