Question

What is the coefficient of x7 in the expansion of (1 + x)11?

Answer 1

You can choose to expand the equation to find the coefficient of x7 but that would take a lot of time. Here is a useful tactic that can help; 

11C(something)(1)(x)⁷ ----> This gives the coefficient of x⁷
11C7(1)⁴(x)⁷ ----> You know that pascal's triangle is equal on both sides 
11C7×1⁴ = coefficient of x⁷ (just ignore x⁷)
330x1⁴=330 

This means that the coefficient of x⁷ is 330. You can double check by expanding the equation. If you do not understand what I did there, you can ask me how I got to the solution. 

Hope I helped :)