# Probability Question

• Sep 16th 2006, 03:01 PM
JaysFan31
Probability Question
A company orders supplies from 10 distributors and wishes to place 7 orders. What is the probability that all of the orders go to different distributors?

The answer is 0.0605, but I'm not sure how you get that. I tried a few things, but I'm not sure. Any help appreciated.
• Sep 16th 2006, 03:09 PM
Plato
That is Permut(10,7)/10^7.
There are 10^7 functions from a set of seven to a set of ten.
If each gets at most one then we have permutations.
These are injections.
• Sep 16th 2006, 03:27 PM
JaysFan31
Ok. Thanks a lot.

Along the same lines, what is the probability that distributor I gets exactly two orders and distributor II gets exactly three orders?

Also, what is the probability that distributors I, II, and III get exactly two, three, and one orders respectively.
• Sep 16th 2006, 04:02 PM
Plato
Quote:

Originally Posted by JaysFan31
Ok. Thanks a lot.

Along the same lines, what is the probability that distributor I gets exactly two orders and distributor II gets exactly three orders?

I probably should have commented in my first reply. We have assumed that the distributors as well as the orders are distinct. The fact that the orders are distinct should have been clearly stated in the question.

Let C(N,k) be combin(N,k).
Distributor I can get two in C(7,2) ways and II can then get three in C(5,3) ways. The remaining can be distributed in 8^2 ways.