5-digit numbers are to be formed using 2, 3, | vedclass

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(D) The set of digits is $\{2, 3, 5, 7, 9\}$. The total number of $5$-digit numbers formed without repetition is $5! = 120$.For $p$: The numbers must

Vedclass · Accepted Answer

$5:3$

Vedclass · Answer

(D) The set of digits is $\{2, 3, 5, 7, 9\}$. The total number of $5$-digit numbers formed without repetition is $5! = 120$.For $p$: The numbers must exceed $20000$. Since all given digits are $\ge 2$,any $5$-digit number formed using these digits will be $\ge 23579$,which is $> 20000$. Thus,$p = 5! = 120$.For $q$: The numbers must lie between $30000$ and $90000$. This means the first digit must be $3, 5,$ or $7$. There are $3$ choices for the first digit. The remaining $4$ positions can be filled by the remaining $4$ digits in $4!$ ways.So,$q = 3 	imes 4! = 3 	imes 24 = 72$.The ratio $p : q = 120 : 72$.Dividing both by $24$,we get $120/24 : 72/24 = 5 : 3$.

$5$-digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ is the number of such numbers that exceed $20000$ and $q$ is the number of those that lie between $30000$ and $90000$,then $p : q$ is

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