determine the number of ways of selecting four letters
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pka
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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.
\(\displaystyle \L \underbrace {\left( {1 + x} \right)^5 }_{\{ p,e,g,m,o\} }\underbrace {\left( {1 + x + x^2 } \right)}_{\{ r\} }\underbrace {\left( {1 + x + x^2 + x^3 } \right)^2 }_{\left\{ {a,l} \right\}}\).
I have explained why each term with an underbrace.