Question
Download Solution PDFIf 2nP3 = 100 nP2, then the value of n is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Permutations and Combinations:
- nPr = \(\rm \frac{n!}{(n - r)!}\).
- n! = 1 × 2 × 3 × ... × n.
- 0! = 1.
Calculation:
Expanding the expression on both sides of the equation, we get:
2nP3 = 100 nP2
⇒ \(\rm \frac{2n!}{(2n - 3)!}=100\frac{n!}{(n - 2)!}\)
⇒ \(\frac{2n (2n - 1) (2n - 2)(2n - 3)!}{(2n - 3)!}=100\times \frac{n(n-1)(n-2)!}{(n-2)!}\)
⇒(2n)(2n - 1)(2n - 2) = 100(n)(n - 1)
⇒ 2n - 1 = 25, n ≠ 1.
⇒ n = 13.
Last updated on Jun 20, 2025
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