Choose the correct answer. A five digit number divisible by 3 is … - Vidyadip

MCQ

Choose the correct answer. A five digit number divisible by $3$ is to be formed using the numbers $0, 1, 2, 3, 4$ and $5$ without repetitions. The total number of ways this can be done is.

✓
$216$
B
$600$
C
$240$
D
$3125$

✓

Answer

Correct option: A.

$216$

We know that a number is divisible by $3$ if the sum of its digits is divisible by $3.$
Now sum of the given six digits is $15$ which is divisible by $3.$
So to form a number of five$-$digit which is divisible by $3$ we can remove either $'O\ '$ or $'3\ '.$
If digits $1, 2, 3, 4, 5$ are used then number of required numbers $= 5!$
If digits $0, 1, 2, 4, 5$ are used then first place from left can be filled in $4$ ways and remaining $4$ places can be filled in $4!$ ways.
So in this case required numbers are $4 \times 4!$ ways.
So, total number of numbers $= 120 + 96 = 216$

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