Question

A $5$ digits numbers divisible by $3$ to be formed the numerals $0,1,2,3,4$ & $5$ without repetition. The total number of ways this can be done is:

• A. $3125$
• B. $600$
• C. $240$
• D. $216$

Answer 1

The correct option is D $216$

If a number is divisible by 3, then the sum of digits is divisible by 3.

No. S=1,2,3,4,5.

Total number of numbers = 5!= 120

No. S=0,1,2,4,5

Total numbers = 5!-4!=120-24=96

There are 4! numbers beginning with 0

$\therefore$ Total number of numbers = 120+96

=216