mathmath333 one year ago In how many ways can 5 prizes can be distributed to 8 students if each student can get any number of prizes ?

1. 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}}

2. anonymous

I can help.

3. anonymous

Lets see... 5/8, correct?

4. mathmath333

it is $$5^{8}$$ not 5/8

5. anonymous

Five to the eighth power? Okay. So your answer is B.

6. mathmath333

lol i dont know answer , i m asking for it

7. anonymous

8. 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 ?

9. anonymous

but @phi what if the first had five prizes at time xD or so hmmm

10. dan815

|dw:1441150449776:dw|

11. 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?

12. dan815

distinguishable prizes eh

13. phi

I am assuming distinguishable prizes.

14. mathmath333

what is default if it is not given (identical or distinct)

15. dan815

if its identical its a stars and bars question, visualize like that drawing

16. dan815

okay there is 1 way to do the non identical case its not that pretty

17. dan815

oh wait its not even choose since the presents are not identical its 8 P

18. 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

19. dan815

ill think about some neater way

20. dan815

later xD