Originally Posted by
Plato Please tell us what is meant by a selection?
POST SCRIPT:
I made a guess as to what this question means.
If one expands $\displaystyle \left( {1 + x} \right)^2 \left( {1 + x + x^2 } \right)\left( {\sum\limits_{k = 0}^3 {x^k } } \right)^2 \left( {\sum\limits_{k = 0}^9 {x^k } } \right)$
we get a polynomial of degree 19.
Each coefficient in the expansion tell the number of possible selections.
For example: the term in the expansion $\displaystyle 191x^9$ tells us that there are 191 ways to select nine items from that list.
If we sum all the coefficients we get $\displaystyle 1920$.
But that includes the empty selection.
Remove it and there is $\displaystyle 1919.$