For fun this semester I decided to take a probability class and doing a lot of the random problems from the book to learn the material. I am finding that sometimes I am over complicating some of these problems. Here is a problem I came across. When I punched in the numbers it didn't seemed valid to me. Unfortunately, the book being used doesn't have odd or even answers in the back of the book. The problem says. "Two new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes. Drug A is to be given to 22 mice, drug B is to be given to another 22 mice, and the remaining 16 mice are to be used as controls. How many ways can the assignment of treatments to mice be made? A single assignment involves specifying the treatment for each mouse -- whether drug A, drug B or no drug." My logic. I asked myself how many different ways can drug A be taken? I say that 22 mice have to be given it and there are 60 mice total. To mean, that means taking n! / r!(n-r)! n is 60 r is 22 Using these values I get this 14,154,280,149,473,100 Seeing that number sent red flags here. Is my logic faulty here? I think it is but looking for some reassurance from others. Thanks.