Question

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

Answer 1

Answer: 95040

Explanation:

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

nCr * r!

12C5 * 5!

792 * 120

= 95040