First slide

Permutations

Question

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

Moderate

A

5 : 4
B

5 : 3
C

8 :3
D

15 : 16

Solution

Any number 5-digit formed by 2, 3, 5, 7, 9, exceeds 20000. Therefore, $p = 5! = 120$
A number will lie between 30000 and 90000 if it begins with 3, 5 or 7
$∴ q = (3) (4!) .$ Thus $p : q = 5 : 3 .$

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