Determine the largest group of people that can meet if no two people have the same three initials. I know that the answer is 17,576 but I don't understand how to set it up, if someone could show steps that would be great. (This is a combinatorics question.)

The manager at gabriela's furniture store is trying to figure out how much to charge for a book shelf that just arrived. the book shelf was bought at a wholesale price of $ 1 4 7 . 0 0 $147.00, and gabriela's furniture store marks up all furniture by 6 0 % 60%. at what price should the manager sell the book shelf?