Learn how Pascal's triangle of binomial coefficients
works:

If we add any two numbers which are side by side, we 
will always get the number which is between and below 
them:



                        0C0=1

                  1C0=1      1C1=1       

              2C0=1     2C1=2     2C2=1

         3C0=1    3C1=3      3C2=3     3C3=1

    4C0=1     4C1=4     4C2=6     4C3=4     4C4=1  


2C1 + 2C2 + 3C2

Add just the first two:

If we add 2C1=2 and 2C2=1, they are side by side, so we
get the number between and below them which is 3C2=3.
Then if we add 3C2 to that we get 2(3C2)=6.

Then we notice that 4C2 also = 6, and 4C2 is a single
binomial coefficient, so the answer is 4C2.

Edwin