Assessment: The Binomial Theorem

What does ⁿCᵣ count?

In every term of the expansion of (a+b)ⁿ, what do the exponents of a and b add up to?

Evaluate ⁷C₂.

Find the 3rd term of (x + 2)⁴. (Give just the numeric coefficient.)

Expand (x + 1)⁴.

Find the coefficient of x² in the expansion of (x + 3)⁴.

A club of 8 members wants to know how many different 3-person committees are possible. Find ⁸C₃.

Why is the binomial theorem more practical than Pascal's triangle for expanding (x+1)²⁰?

Find the 5th term of (x + 2)⁶. (Give just the numeric coefficient.)

Find the coefficient of x⁵ in the expansion of (x + 1)⁷.