5-digit numbers are to be formed using 2, 3, 5, 7, 9 without repeating the digits.

Question

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:

Accepted Answer

$p$: all numbers formed exceed 20000 automatically since the smallest possible first digit is 2 and smallest arrangement 23579>20000: $p=5!=120$.

$q$: numbers between 30000 and 90000, so first digit $\in\{3,5,7\}$ (excluding 2 and 9): $3	imes4!=72$.

$p:q = 120:72 = 5:3$

Solutions · 1