# Thread:

1. ## Help needed on combination problem

Prove that the total number of selectionsthat can be made out of the letters "DADDY DID A DEADLY DEED" is 1919.

does anyone have the solution to this??
-thank you

2. ## Re: Help needed on combination problem

Originally Posted by blackhat98
Prove that the total number of selectionsthat can be made out of the letters "DADDY DID A DEADLY DEED" is 1919.
does anyone have the solution to this??
Please tell us what is meant by a selection?

POST SCRIPT:
I made a guess as to what this question means.
If one expands $\left( {1 + x} \right)^2 \left( {1 + x + x^2 } \right)\left( {\sum\limits_{k = 0}^3 {x^k } } \right)^2 \left( {\sum\limits_{k = 0}^9 {x^k } } \right)$
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 $191x^9$ tells us that there are 191 ways to select nine items from that list.
If we sum all the coefficients we get $1920$.
But that includes the empty selection.
Remove it and there is $1919.$

Nice method!

4. ## Re: Help needed on combination problem

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 $\left( {1 + x} \right)^2 \left( {1 + x + x^2 } \right)\left( {\sum\limits_{k = 0}^3 {x^k } } \right)^2 \left( {\sum\limits_{k = 0}^9 {x^k } } \right)$
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 $191x^9$ tells us that there are 191 ways to select nine items from that list.
If we sum all the coefficients we get $1920$.
But that includes the empty selection.
Remove it and there is $1919.$
thank you Plato....
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