Question

Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):

• A. 1023
• B. 1024
• C. 511
• D. 2047
• E. 612

Hint:

The sum of all binomial coefficients for a given \( n \) is \( 2^n \). To exclude \( \binom{n}{0} \), subtract 1.

Answer 1

The Correct Option is B

Using the binomial theorem, the sum of binomial coefficients from \( k = 1 \) to \( k = n \) is: \[ \sum_{k=1}^{10} \binom{10}{k} = 2^{10} - 1 \] \[ = 1024 - 1 = 1023 \]