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:
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:
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Every number exceeds 20000; for q the first digit must be 3, 5 or 7.
Updated On: Nov 4, 2026
- 6 : 5
- 3 : 2
- 4 : 3
- 5 : 3
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The Correct Option is D
Solution and Explanation
All digits are at least 2 and the numbers have 5 distinct digits from the 5 available, so every number is at least 23579 \(\gt 20000\). Thus \(p = 5! = 120\).
Numbers between 30000 and 90000 must start with 3, 5 or 7 (starting with 2 gives less than 30000, starting with 9 gives more than 90000).
\(q = 3\times 4! = 72\).
\(p:q = 120:72 = 5:3\).
Answer: (4) 5 : 3
Numbers between 30000 and 90000 must start with 3, 5 or 7 (starting with 2 gives less than 30000, starting with 9 gives more than 90000).
\(q = 3\times 4! = 72\).
\(p:q = 120:72 = 5:3\).
Answer: (4) 5 : 3
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