Question

How many four-digit numbers divisible by $10$ can be formed using $1,5,0,6,7$ without repetition of digits?

• A. $24$
• B. $36$
• C. $44$
• D. $64$

Answer 1

Answer: (A)

$24$

Four digit numbers divisible by ${}^{\prime }{10}^{\prime }$ using $1,5,0,6,7$

Divisibility by ${}^{\prime }{10}^{\prime }\to$ no. should end with zero

$\underset{\underset{4}{\uparrow }}{-}$ After fixing 'zero' at unit place, we are left with ${}^{\prime }{4}^{\prime }$ nos.

$\underset{\underset{3}{\uparrow }}{-}$ After placing any no at tens place we are left with ${}^{\prime }{3}^{\prime }$ nos.

$\underset{\underset{2}{\uparrow }}{-}$ After placing any no at tens and hundred place

$Total=4\times 3\times 2$

$=24$.