What is the probability that only 2 colors are chosen?

In summary, the conversation discusses the probability of only 2 colors being chosen when n people choose at random from a set of C available colors. The solution involves finding the number of ways for 2 colors to be chosen and calculating the number of onto functions from a set of size n to a set of size 2. The latter can be represented as a bit string and the solution is eventually solved by the participants.
  • #1
bob j
22
0
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
 
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  • #2


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?
 
  • #3


never mind, I solved it ;)
 
  • #4


Great
 

1. What is the definition of probability?

Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. How is probability calculated?

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

3. What is the probability of choosing only 2 colors from a set of colors?

The probability of choosing only 2 colors from a set of colors depends on the total number of colors in the set. For example, if there are 6 colors in the set, the probability would be 2/6 or 1/3.

4. How do you calculate the total number of possible outcomes?

The total number of possible outcomes can be calculated by multiplying the number of options for each choice together. For example, if there are 5 colors and you want to choose 2, the total number of possible outcomes would be 5*4 = 20.

5. Can the probability of choosing only 2 colors be greater than 1?

No, the probability cannot be greater than 1. A probability of 1 indicates certainty, meaning the event is guaranteed to occur. Any probability greater than 1 would not make sense.

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