TS EAMCET · Maths · Permutation Combination
The least value of the natural number \(n\) satisfying \(C(n, 5)+C(n, 6)>C(n+1,5)\) is
- A \(10\)
- B \(11\)
- C \(12\)
- D \(13\)
Answer & Solution
Correct Answer
(B) \(11\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { We have, }{ }^n C_5+{ }^n C_6>{ }^{n+1} C_5 \\ & { }^{n+1} C_6>{ }^{n+1} C_5 \\ & \Rightarrow \quad \frac{(n+1) !}{6 !(n+1-6) !}>\frac{(n+1) !}{5 !(n+1-5) !} \\ & \Rightarrow \quad 5 !(n-4) !>6 !(n-5) ! \\ & \Rightarrow \quad 5 !(n-4)(n-5) !>6 \cdot 5…
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