5 - digit numbers are to be formed using $2,3,5,7$, 9 without repeating the digits. If $p$ be the number of…
5 - digit numbers are to be formed using $2,3,5,7$, 9 without repeating the digits. If $p$ be the number of such numbers that exceed 20000 and $q$ be the number of those that lie between 30000 and 90000 , then $p: q$ is:
$6: 5$
$3: 2$
$4: 3$
$5: 3$
Solution
$\mathrm{p}: \begin{array}{llllll}0 & 0 & 0 & 0 & 0 & \text { place } \\ 5 & 4 & 3 & 2 & 1 & \text { ways }\end{array}$
Total no, of ways $=5 !=120$
Since all numbers are $>20,000$
$\therefore$ all numbers $2,3,5,7,9$ can come at first place.
$\mathrm{q}: \begin{array}{llllll}0 & 0 & 0 & 0 & 0 & \text { place } \\ 3 & 4 & 3 & 2 & 1 & \text { ways }\end{array}$
Total no. of ways $=3 \times 4 !=72$
( $\because 2$ and 9 can not be put at first place)
So, $p: q=120: 72=5: 3$