JEE Mains · Maths · STD 11 - 6. permutation and combination
\(\sum \limits_{ k =0}^6{ }^{51- k } C _3\) is equal to
- A \({ }^{51} C _4-{ }^{45} C _4\)
- B \({ }^{51} C _3-{ }^{45} C _3\)
- C \({ }^{52} C _4-{ }^{45} C _4\)
- D \({ }^{52} C _3-{ }^{45} C _3\)
Answer & Solution
Correct Answer
(C) \({ }^{52} C _4-{ }^{45} C _4\)
Step-by-step Solution
Detailed explanation
\(\sum \limits_{ k =0}^6{ }^{51- k } C _3\) \(={ }^{51} C _3+{ }^{50} C _3+{ }^{49} C _3+\ldots+{ }^{45} C _3\) \(={ }^{45} C _3+{ }^{46} C _3+\ldots \ldots+{ }^{51} C _3\) \(={ }^{45} C _4+{ }^{45} C _3+{ }^{46} C _3+\ldots \ldots+{ }^{51} C _3-{ }^{45} C _4\)…
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