There're 5 students and 5 colours.
(Lets say Red, Yellow, Green, Blue, Purple)
Each student picks a colour independently (uniformly at random).
What is the probability that, only (1,2,3,4,5) colours are picked respectively?

(E.g.
Only one colour is picked:
Student (1,2,3,4,5) - Colour (Red, R,R,R,R)
Only two colour is picked:
Student (1,2,3,4,5) - Colour (Red,R,R,R,Yellow))

Question

There're 5 students and 5 colours.
(Lets say Red, Yellow, Green, Blue, Purple)
Each student picks a colour independently (uniformly at random).
What is the probability that, only (1,2,3,4,5) colours are picked respectively?

(E.g.
Only one colour is picked: 
Student (1,2,3,4,5) -> Colour (Red, R,R,R,R)
Only two colour is picked:
Student (1,2,3,4,5) -> Colour (Red,R,R,R,Yellow))

hail · Answer

My calculator says its about Shfifty five percent.

anonymous · Answer

Actually I'm told to find the expected number of colour being picked...
So I want to know the respect probability that each number of colour is being picked.

anonymous · Answer

1/5^5 for one
2^5/5^5  for two
3^5/5^5 for three
4^5/5^5 for four
1 for five

anonymous · Answer

I got similar approach with 5^5.... But for example, 
1 colour you have (RRRRR)(GGGGG)(BBBBB)(YYYYY)(PPPPP)
2 colours you have (RRRRG)(RRRGR)(RRGRR)(RRGRR)...etc

I tried to approach with permutation and combination but 5 colours don't add up to be 5^5

anonymous · Answer

no consider it like number filling problem type
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