Question

Total $5$ -digit numbers divisible by $6$ can be formed using $0,1,2,3,4,5$ if repetition of digits is allowed is:

• A. $60$
• B. $48$
• C. $108$
• D. $4680$

Answer 1

Answer: (D)

$4680$

The 5 digit numbers should have only digits$0,1,2,3,4or5.$

Let the number be $abcde.$

First number with $5$ digits divisible by $6:10002.$

Last number with $5$ digits divisible by $6:55554$

Numbers with $100$ as prefix:

$abc=100.de=02,14,20,32,44,50$

$abc=101de=04,10,22,34,40,52$

$abc=102de=00,12,24,30,42,54$ : :

$abc=155de=04,10,22,34,40,52$

So between $10000$ to $19999$ we have $156\times 6=936$ numbers.

Similarly between$20000$ to $29999$ we have also $156\times 6=936$ numbers.

Total number : $936\times 5=4680$

Hence, the option $D$ is the correct answer.