To solve this problem, we can use the formula for the number of handshakes in a group of people.
Let's assume that there are 'n' people at the party. Each person shakes hands with 'n-1' other people (excluding themselves).
So, the total number of handshakes can be calculated using the formula:
Total number of handshakes = (n * (n-1)) / 2
Given that there were 66 handshakes, we can set up the equation:
66 = (n * (n-1)) / 2
To solve this equation, we can multiply both sides by 2 to get rid of the fraction:
132 = n * (n-1)
Next, we can rearrange the equation to get a quadratic equation:
n^2 - n - 132 = 0
Now, we can factorize the quadratic equation:
(n - 12)(n + 11) = 0
Setting each factor equal to zero, we get two possible solutions:
n - 12 = 0 or n + 11 = 0
Solving for 'n', we find:
n = 12 or n = -11
Since the number of people cannot be negative, we discard the solution n = -11.
Therefore, the number of people at the party is 12.
So, the correct answer is B) 12 people.