Question

If $m$ number of integers greater than $7000$ can be formed with the digits $3,5,7,8$ and $9,$ such that no digit is being repeated, then the value of $\frac{m}{100}$ is

Answer 1

Answer: 1.92

A five digit integer is always greater than $7000.$
The number of such integers are ${}^5{P}_5=5!=120.$
For a four digit integer to be greater than $7000,$ it must begin with $7,8$ or $9.$
The number of such integers are ${\left(3\right)}^4{P}_3=72.$
Hence, the required number of such integers are $120+72=192.$
$\Rightarrow m=192$
$\Rightarrow \frac{m}{100}=\mathrm{1.92.}$