What is the probability that only 2 colors are chosen?

[bob j]

Hi all,
I have the following problem. n people choose a color at random. There are C available colors, from 1 to C, for each node.

What is the probability that only 2 colors are chosen?

thanks

 

[mXSCNT]

Well, to find the number of ways for the total number of colors chosen to be exactly 2, first pick the pair of colors, which can be done in C(C,2) ways, with C(,) being choose. Then count the number of onto functions from a set of size n to a set of size 2.

You could find the latter as follows: every function from a set of size n to a set of size 2, can be represented as a bit string of length n, containing at least one 0 and at least one 1. How many such bit strings are there?

 

[bob j]

never mind, I solved it ;)

 

[mXSCNT]

Great