Line up the 21 red balls in a row: RRRRRRRRRRRRRRRRRRR
Place a space on either side of each red ball: _R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_R_

Important: Each available space is a potential location for a blue ball. This ensures that no two blue balls are together.
There are 22 spaces in total.
We'll select 19 of those 22 spaces and place a blue ball in each selected space.
So the question becomes, "In how many different ways can we select 19 spaces from 22 spaces?"
Since the order in which we select the 19 spaces does not matter, we can use combinations.

We can select 19 spaces from 22 spaces in 22C19 ways.
22C19 = 22!/(19!)(3!)

Answer: A