`\ ^5C_1+\ ^5C_2+\ ^5C_3+\ ^5C_4+\ ^5C_5` is equal to `30` b. `31` c. `32` d. 33

Explanation

To solve the expression \( \binom{5}{1} + \binom{5}{2} + \binom{5}{3} + \binom{5}{4} + \binom{5}{5} \), we can follow these steps:

### Step 1: Understand the Binomial Coefficient
The binomial coefficient \( \binom{n}{r} \) represents the number of ways to choose \( r \) elements from a set of \( n \) elements.

### Step 2: Write the Full Summation
We can express the sum as:
\[
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