mathmath333
  • mathmath333
In how many ways can 5 prizes can be distributed to 8 students if each student can get any number of prizes ?
Mathematics
katieb
  • katieb
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{ In how many ways can 5 prizes can be distributed to 8 students}\hspace{.33em}\\~\\ & \normalsize \text{ if each student can get any number of prizes ?}\hspace{.33em}\\~\\ & a)\ 40 \hspace{.33em}\\~\\ & b)\ 5^{8} \hspace{.33em}\\~\\ & c)\ 8^{5} \hspace{.33em}\\~\\ & d)\ 120 \hspace{.33em}\\~\\ \end{align}}\)
anonymous
  • anonymous
I can help.
anonymous
  • anonymous
Lets see... 5/8, correct?

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mathmath333
  • mathmath333
it is \(5^{8}\) not 5/8
anonymous
  • anonymous
Five to the eighth power? Okay. So your answer is B.
mathmath333
  • mathmath333
lol i dont know answer , i m asking for it
anonymous
  • anonymous
Your answer is B. : )
phi
  • phi
the first prize can go to any of 8 people the 2nd prize can go to any of 8 people etc, .... how about 8^5 ?
anonymous
  • anonymous
but @phi what if the first had five prizes at time xD or so hmmm
dan815
  • dan815
|dw:1441150449776:dw|
wolf1728
  • wolf1728
There are 8 ways that all 5 prizes can be given to 1 person Now for giving 4 prizes to 1 person and 1 prize to 1 person Would that be 8*7 ways or 56?
dan815
  • dan815
distinguishable prizes eh
phi
  • phi
I am assuming distinguishable prizes.
mathmath333
  • mathmath333
what is default if it is not given (identical or distinct)
dan815
  • dan815
if its identical its a stars and bars question, visualize like that drawing
dan815
  • dan815
okay there is 1 way to do the non identical case its not that pretty
dan815
  • dan815
oh wait its not even choose since the presents are not identical its 8 P
dan815
  • dan815
________ 5 presents, in 8 different spots = 8 ways presents 4,1 in 2 spots, = 8 p 2 * 5 choose 4 presents 3,2 , 8 p 2 * 5 chose 3 * 4 choose 2 3,1,1, 8 p 3 * 5 choose 3* 4 choose 1 * 3 choose 1 2,2,1 ... complete these 2,1,1,1 1,1,1,1,1 add em all up
dan815
  • dan815
ill think about some neater way
dan815
  • dan815
later xD

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