JEE Main · MathematicsEasy

$Find the value of^{4} C_{0} +^{4} C_{1} +^{4} C_{2} +^{4} C_{3} +^{4} C_{4} .$

A. $8$
B. $16$
C. $32$
D. $64$

Show correct answer & step-by-step solution

Correct answer: B — $16$

Solution

The sum of binomial coefficients^{n} C_{0} +^{n} C_{1} + \dots +^{n} C_{n} is equal to 2^{n} . For n = 4, the sum is 2^{4}, which equals 16 .

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