Question

Total $5-$digits numbers divisible by $6$ can be formed using $0,1,2,3,4,5$ if repetition of digits is not allowed is:

• A. $60$
• B. $48$
• C. $108$
• D. $216$

Answer 1

The correct option is C $108$

$5-$digits numbers divisible by $6$ can be formed using $0,1,2,3,4,5$

we have to use 1,5 and 2,4 as pairs so, we can put 0,3 as 5th no.

we can put only even digit at last

Taking 0

let 0 be ones place digit

$\Rightarrow 4\times 3\times 2\times 1=24$

when last digit not 0

$\Rightarrow 2\times 3\times 3\times 2\times 1=36$

Taking 3

$\Rightarrow 2\times 4\times 3\times 2\times 1=48$

Total$=24+36+48=108$