JEE Mains · Maths · STD 11 - 6. permutation and combination
The value of \(\sum \limits_{ r =0}^{20}{ }^{50- r } C _{6}\) is equal to
- A \({ }^{51} C _{7}+{ }^{30} C _{7}\)
- B \({ }^{51} C _{7}-{ }^{30} C _{7}\)
- C \({ }^{50} C _{7}-{ }^{30} C _{7}\)
- D \(^{50} C _{6}-{ }^{30} C _{6}\)
Answer & Solution
Correct Answer
(B) \({ }^{51} C _{7}-{ }^{30} C _{7}\)
Step-by-step Solution
Detailed explanation
\(\sum_{r=0}^{20}{ }^{50-r} C_{6}={ }^{50} C_{6}+{ }^{49} C_{6}+{ }^{48} C_{6}+\ldots . .+{ }^{30} C_{6}\) \(={ }^{50} C_{6}+{ }^{49} C_{6}+\ldots . .+{ }^{31} C_{6}+\left({ }^{30} C_{6}+{ }^{30} C_{7}\right)-{ }^{30} C_{7}\)…
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