Your class is in groups, working on a combinatorics worksheet. One of the questions asks how many possible ways 5 books out of a
box of 12 can be placed on a shelf. Your classmate suggests you calculate 12C5, which is 792. What would you say to explain how this suggestion is flawed, and how would you help correct them
It is important to note that selection and arrangement are two different things in permutation and combination study. In the scenario above, we have 12 books, out of which 5 is to be arranged on a shelf. The answer prescribed by 12C5 which gives 792, only solves the selection process of choosing 5 books from a total of 12. Every 5 books picked will also have to be arranged on the shelf which is solved as n!(number of ways of arranging n different objects)
Hence, to arrange 5 books from a total of 12 books on a book shelf is
