TS EAMCET · Maths · Binomial Theorem
A student is allowed to select at most \(\mathrm{n}\) books from a collection of \((2 n+1)\) books. If the total number of ways in which ne can select at least one book is 255 , then the value of \(\mathrm{n}\) is
- A \(4\)
- B \(5\)
- C \(6\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \quad{ }^{2 n+1} C_1+{ }^{2 n+1} C_2+\ldots . .+{ }^{2 n+1} C_n=255 (i)\\ & \because{ }^n C_r={ }^n C_{n-r} \\ & { }^{2 n+1} C_{2 n}+{ }^{2 n+1} C_{2 n-1}+\ldots .+{ }^{2 n+1} C_{n+1}=255 (ii) \end{aligned} \] Add (i) and (ii),…
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