Let S be the sample space of all five digit numbers. If p is the...

Given, five-digit number,

So $n\left(S\right) =$total $5$ digit number will be$= 9 \times {10}^{4}$

Now let $A:$ number is multiple of $7$ but not divisible by $5$

Smallest $5$ digit divisible by $7$ is $10003$

Largest $5$ digit divisible by $7$ is $99995$

Now by using ${n}^{th}$ term of A.P formula we have,

$∴ 99995 = 10003 + \left(n - 1\right)7$

$⇒ n = 12857$

Now finding number which is divisible by $35$

Again using A.P formula we have,

$99995 = 10010 + \left(P - 1\right)35$

$⇒ P = 2572$

Now number divisible by $7$ but not by $35$ are

$12857 - 2572 = 10285$

So, probability will be $P = \dfrac{10285}{90000}$

And $9P = 1 . 0285$