I am new to combinatorics and I'm reading it from Kenneth H.Rosen book. Under the topic Product rule of counting, this problem was given :
A new company with just two employees, Sanchez and Patel, rents a
floor of a building with 12 offices. How many ways are there to assign
different offices to these two employees?
The answer is 12*11=132 ways
By the definition of product rule,
Suppose that a procedure can be broken down into a sequence of two
tasks. If there are n 1 ways to do the first task and for each of
these ways of doing the first task, there are n 2 ways to do the
second task, then there are n 1. n 2 ways to do the procedure.
So I think it should be 12(for Sanchez) * 12(for Patel) =144.
Please explain what mistake I was doing in a detailed manner. Thank You.
Best Answer
You count the office you've given to Sanchez as a possibility for Platel, something you shouldn't do as the question states that there are different offices.