determine the number of ways of selecting four letters

Hi, I need help with this question

determine the number of ways of selecting four letters , with ought regard for
the order, form the work parallelogram.


13C4-13C3-13C3=143


the answer is supposed to be 150....


thanks

Expand the following polynomial and you will find the coefficient of x<SUP>4</SUP> is 150.
\(\displaystyle \L \underbrace {\left( {1 + x} \right)^5 }_{\{ p,e,g,m,o\} }\underbrace {\left( {1 + x + x^2 } \right)}_{\{ r\} }\underbrace {\left( {1 + x + x^2 + x^3 } \right)^2 }_{\left\{ {a,l} \right\}}\).

I have explained why each term with an underbrace.

^ Thanks pka