Question

$5$ - 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:

• A. 6 : 5
• B. 3 : 2
• C. 4 : 3
• D. 5 : 3

Answer 1

Answer: (D)

$p:\begin{array}{cccccc}0& 0& 0& 0& 0& place\\ 5& 4& 3& 2& 1& ways\end{array}$
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.
$q:\begin{array}{cccccc}0& 0& 0& 0& 0& place\\ 3& 4& 3& 2& 1& ways\end{array}$
Total no. of ways = 3 x 4 ! = 72
$\left(\because 2and9cannotbeputatfirstplace\right)$
So, $p:q=120:72$ = $5:3$