Question

Find the number of four digit numbers that are divisible by $15$ and formed with the digits $0,1,2,3,4,5$ when repetition is not allowed.

• A. $25$
• B. $34$
• C. $40$
• D. $55$

Answer 1

The correct option is B $34$

A $4$ digit number formed $0,1,2,3,4,5$ is divisible by $15$, then it ends with $0$ or $5$

Repetition not allowed

(1) Case : 1 : Ends with $0$

First three sum should be divisible by $3$

$(1,2,3)$

$(2,3,4)$

$(1,3,5)(3,4,5)$

Case : 2: Ends with $5$

$(0,1,3,5)(1,2,4,5)$

Total ways $=\left(3\right)!5+4=34$

Hence the correct answer is $34$