Find the sum of²¹C₀ +²¹C₁ +²¹C₂ +²¹C₃ +²¹C₄ + .......... +²¹C₁₀.

Dear Student,
Please find below the solution to the asked query:
$$\begin{gathered} {}^{21}{C}_0{+}^{21}{C}_1{+}^{21}{C}_2{+}^{21}{C}_3{+}^{21}{C}_4+...{+}^{21}{C}_{10} \\ =1+21+\frac{21\times 20}{1\times 2}+\frac{21\times 20\times 19}{1\times 2\times 3}+\frac{21\times 20\times 19\times 18}{1\times 2\times 3\times 4}+...+\frac{21\times 20\times 19\times 18\times ...\times 12}{1\times 2\times 3\times 4\times ...\times 10} \end{gathered}$$
Hope this information will clear your doubts about Binomial theorem.
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