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Binomial Theorem — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBinomial Theorem4 Marks
Question
Evaluate $^{20}\text{C}_{5}+\sum\limits_\text{r=2}^5\ ^{25-\text{x}}\text{C}_4.$
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Answer

We have, $\Rightarrow\ ^{20}\text{C}_{5}+\sum\limits_\text{r=2}^5\ ^{25-\text{x}}\text{C}_4$ $\Rightarrow\ \big(^{20}\text{C}_{5}+{^{20}\text{C}_{4}}\big)+{^{21}\text{C}_{4}+^{22}}\text{C}_{4}+{^{23}\text{C}_{4}}$ $\Rightarrow\ \big(^{21}\text{C}_{5}+{^{21}\text{C}_{4}}\big)+{^{22}\text{C}_{4}}+{^{23}\text{C}_{4}}$ $\Rightarrow{^\text{23}}\text{C}_{\text{5}}+{^\text{23}}\text{C}_{\text{4}}$ $\Rightarrow{^\text{24}}\text{C}_{\text{5}}$ $\Rightarrow 42504$

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