Question

\(\sum_{k=0}^{10} {}^{20}C_k\) is equal to

• A. \(2^{19} + \frac{1}{2} {}^{20}C_{10}\)
• B. \(2^{19}\)
• C. \({}^{20}C_{10}\)
• D. None of these

Hint:

Use \(\sum_{k=0}^n \binom{n}{k} = 2^n\) and symmetry \(\binom{n}{k} = \binom{n}{n-k}\).

Answer 1

The Correct Option is A