Question

How many $3$ digit numbers can be formed from the digits $2,3,5,6,7,9$ which are divisible by $5$ and none of the digits is repeated?

• A. $5$
• B. $10$
• C. $15$
• D. $20$

Answer 1

Answer: (D)

$20$

Since the number should be divisible by $5$ the last digit must be $5.$ The first $2$ digits can be choosen from remaining $5$ numbers and rearranged.

$\Rightarrow$ Total combinations $={}^5{C}_2\times 2!$

$=10\times 2$

$=20.$

Hence, the answer is $20.$