a typical physician performs 4,000 procedures/services per year. These are made up of 75 unique procedures/services. If I were to select 30 line items (each being a reported service or procedure), what is the probability that each of the 30 in the sample would represent one of those 75 unique services or procedures such that each of the 30 were a unique service/procedure? Thank you for your help and feel free to respond to me directly at fcohen7777@gmail.com

Last edited by Slade Steele; 10-12-2015 at 06:11 PM.
Reason: Clarify the question

Not totally following your question. The probability of selecting procedure would be the number of those procedures over the total number of procedures.

Once you select one then you just adjust your numbers. Please provide a little more clarity. Thanks.

For the problem itself, if a certain procedure/services is allowed to be not performed in a year, then the number 4000 is redundant and you just need to model by a multinomial distribution.

In such case the probability of having a specific 30 procedure to appear exactly once each will be

For the generic case, you multiply the above probability by

However, things become more complicated if you are given that they must happen once each in the 4000 procedures. You are now facing truncated version of multinomial distribution. Let see the above fits your model or not first.