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mathmath333
 one year ago
counting question
mathmath333
 one year ago
counting question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} & \normalsize \text{How many different sums can be formed by the following }\ ?\hspace{.33em}\\~\\ & \normalsize 5\ \text{dollar},\ 1\ \text{dollar},\ 50\ \text{cents},\ 25\ \text{cents},\ 10\ \text{cents},\ 3\ \text{cents},\ 2\ \text{cents},\ 1\ \text{cent.} \hspace{.33em}\\~\\ \end{align}}\)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0I guess if you take 2 at a time its 8C2 right?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0the 3 at a time it will be 8C3

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0yes u can also take 3 ,4, 5 upto 8 at a time

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0yes  but could there be any duplicates in all these?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0just need to deduct the double count like example 2 cent and 1 cent taken both are equal to 3 cent taken once

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0and of course there is 8C1 singles

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} & \dbinom{8}{1}+\dbinom{8}{2}+\cdots+\dbinom{8}{8}=2^{8}1 \hspace{.33em}\\~\\ \end{align}}\)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0i think the only duplicates are the ones you mentioned

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0yes but consider 5 dollar +1cent +2 cent =5 dollar+3cent

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0this also duplication

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0and 1 dollar + 3 , 1 dollar + 1 + 2

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0yes all are considered

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0 also same for 50 , 25, 10 cents

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0only combinations we are concerned with here right? not permutations

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0 yes  bacuase we are dealing with sums only

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0yes only addition (result) is counted

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0that identity, = 2^8  1 I haven't seen that before.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0google sum of combinations u will get it

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0https://www.physicsforums.com/threads/sumofcombinations.83309/

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0right so how do we go about counting the number of duplicates?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0yea i m confused about that the main thing
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