Question
Download Solution PDFIf nP4: n-1P3 = 9:1, then find the value of n?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF
Given:
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nP4 : n-1P3 = 9 : 1
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We need to find the value of n.
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Formula for permutations: nPr = n! / (n - r)!
Concept Used:
The ratio of permutations is given as nP4 : n-1P3.
Substituting the formula for permutations, we solve step-by-step:
Calculation:
Using the formula for permutations:
nP4 = n! / (n - 4)!
(n - 1)P3 = (n - 1)! / (n - 1 - 3)! = (n - 1)! / (n - 4)!
Substituting in the ratio:
nP4 : n-1P3 = 9 : 1
⇒ [n! / (n - 4)!] : [(n - 1)! / (n - 4)!] = 9 : 1
Cancelling (n - 4)! from numerator and denominator:
⇒ [n!] : [(n - 1)!] = 9 : 1
Now, n! = n × (n - 1)!
Substituting into the equation:
⇒ [n × (n - 1)!] : [(n - 1)!] = 9 : 1
Cancelling (n - 1)! from both sides:
⇒ n : 1 = 9 : 1
⇒ n = 9
Conclusion:
∴ The value of n is 9.
Last updated on Jul 1, 2025
-> The Indian Army has released the Exam Date for Indian Army Havildar SAC (Surveyor Automated Cartographer).
->The Exam will be held on 9th July 2025.
-> Interested candidates had applied online from 13th March to 25th April 2025.
-> Candidates within the age of 25 years having specific education qualifications are eligible to apply for the exam.
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