COMEDK · Maths · 7. Binomial Theorem
If \({ }^{\mathrm{n}+2} \mathrm{C}_8:{ }^{\mathrm{n}-2} \mathrm{P}_4=57: 16\), then ' n ' is
- A 21
- B 17
- C 19
- D 20
Answer & Solution
Correct Answer
(C) 19
Step-by-step Solution
Detailed explanation
The given ratio is \(\dfrac{^{n+2}C_{8}}{^{n-2}P_{4}} = \dfrac{57}{16}\). Using the definitions \(^{n}C_{r} = \dfrac{n!}{r!(n-r)!}\) and \(^{n}P_{r} = \dfrac{n!}{(n-r)!}\), we have: \(\dfrac{(n+2)!}{8!(n-6)!} \times \dfrac{(n-6)!}{(n-2)!} = \dfrac{57}{16}\) Simplifying the…
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