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)

$p:\begin{matrix}0&0&0&0&0&place\\ 5&4&3&2&1&ways\end{matrix}$
Total no. of ways = 5 ! = 120
Since all numbers $are > 20,000$
$\therefore \quad$ all numbers $2,3,5, 7,9$ can come at first place.
$q:\begin{matrix}0&0&0&0&0&place\\ 3&4&3&2&1&ways\end{matrix}$
Total no. of ways = 3 x 4 ! = 72
$\left(\because\,2 \,and \,9 can\, not\, be\, put \,at \,first \,place\right)$
So, $p : q = 120 : 72$ = $5 : 3$