WBJEE · Maths · Permutation Combination
The value of the expression \({ }^{47} \mathrm{C}_4+\sum_{\mathrm{j}=1}^5{ }^{52-\mathrm{j}} \mathrm{C}_3\) is
- A \({ }^{52} \mathrm{C}_3\)
- B \({ }^{51} \mathrm{C}_4\)
- C \({ }^{52} \mathrm{C}_4\)
- D \({ }^{51} C_3\)
Answer & Solution
Correct Answer
(C) \({ }^{52} \mathrm{C}_4\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { }{ }^{47} \mathrm{C}_4+{ }^{51} \mathrm{C}_3+{ }^{50} \mathrm{C}_3+{ }^{49} \mathrm{C}_3+{ }^{48} \mathrm{C}_3+{ }^{47} \mathrm{C}_3 \\ & ={ }^{48} \mathrm{C}_4+{ }^{48} \mathrm{C}_3+{ }^{49} \mathrm{C}_3+{ }^{50} \mathrm{C}_3+{ }^{51} \mathrm{C}_3…
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