Count functions from power set of {0,1,...,9} to {a,b,c}

[ParisSpart]

i would like to have some help here.. it is a problem in probabilities i can not find anyway to start finding the functions any ideas and help will be apriciated.



How many functions are there from the power set of all (0,1,2,...,9) with values in total (a,b,c)?
The number is too large. Write your answer as the (natural-based e) logarithm of that number with one digit precision (it should the first digit to the right of the decimal point is correct).

 

[chiro]

Hey ParisSpart.

What kind of functions can you have? Do you have some specific template that you have to follow?

 

[tiny-tim]

Hi ParisSpart!

… with values in total (a,b,c)?

I don't understand this …

what does "in total" mean? ​

 

[ParisSpart]

it means in the set of numbers:(a,b,c)

 

[tiny-tim]

hmm … whyever did you write "in total" then?

ok, for any set X with n elements, how many functions are there from the set X to the set {a,b,c} ?

 

[ParisSpart]

yea... and its says that the number is too big and we must write it like :xxxxxxxxe

 

[tiny-tim]

for any set X with n elements, how many functions are there from the set X to the set {a,b,c} ?

 

[ParisSpart]

dont know :D

 

[tiny-tim]

for any set X with n elements, and for any set Y with m elements,

how many functions are there from the set X to the set Y ?

 

[ParisSpart]

i will multiply m with n?

 

[tiny-tim]

are you guessing?

why do you think that should work?​

 

[ParisSpart]

i don't have any idea for this quiz i need some guides...for finding the solution..

 

[tiny-tim]

ok, try it for X = {0,1} and Y = {a,b,c,d,e,f} …

(ie n = 2, m = 6)

how many functions from X to Y? ​

 

[ParisSpart]

i think 12

 

[tiny-tim]

ok, if there's only 12 you can easily write them out …

write out 12 functions from {0,1} to {a,b,c,d,e,f}