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

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 $120+72=192.$
$\Rightarrow m=192$
$\Rightarrow \frac{m}{100}=1.92.$