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A five-digit number divisible by 3 is to...

A five-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4, and 5, without repetition. The total number of ways this can done is a.`216` b. `240` c. `600` d. `3125`

A

216

B

240

C

600

D

3125

Text Solution

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The correct Answer is:
A
Since, a five-digit number is formed using the digits {0, 1, 2, 3, 4 and 5} divisible by 3 i.e. only possible when sum of the digits is multiple of three.
Case I Using digits 0, 1, 2, 4, 5
Number of ways `= 4 xx 4 xx 3 xx 2 xx 1 = 96`
Case II Using digits 1, 2, 3, 4, 5
Number of ways `= 5 xx 4 xx 3 xx 2 xx 1 = 120`
`therefore` Total numbers formed = 120 + 96 = 216
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