Question

$5$- digit numbers are to be formed using $2,$ $3,$ $5,$ $7,$ $9$ without pepeating 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. $3:5$
• C. $4:3$
• D. $5:3$

Answer 1

The correct option is D $5:3$

$p=5!$ (as every combination of these numbers will be greater than $20000$ , as the least number that can be formed is $23579$)

Now, $q=4!+4!+4!=3.4!$

(as for the number to be greater than 30000 and less than 90000

First digit of the numbers should be 3 or 5 or 7 and remaining digits can be arranged in any order,

$3$_ _ _ _ $=4!$

$5$_ _ _ _ $=4!$

$7$_ _ _ _ $=4!$

Hence Total number of ways = 3.4! )

Now, $\frac{p}{q}=\frac{5!}{3.4!}=\frac{5}{3}$