# MDM4U Combinatorics (Counting) Practice 2016-02-10

I showed you the Indirect Method for counting. In a counting problem if there are some outcomes that are “good” and some that are “bad”, we have

For example, if you have a boxed set of Harry Potter novels, how many different ways can you arrange them on a shelf so they are in the wrong order?

Counting that directly is pretty difficult. You end up trying to count a bazillion cases, and it’s really easy to make a mistake.

BUT we can count it indirectly. In this situation, the relationship is

Total arrangements = (In order) + (Out of order)

We know that the total number of arrangements is $P(7,7)=7!=5040$, and there is only 1 way to correctly arrange the books. So

Total arrangements = (In order) + (Out of order)

5040 = 1 + (Out of order)

or

Out of order = 5040 – 1 = 5039.

## Classwork/Homework

I assigned a bunch of questions and gave you 35 minutes in class to get started. Here is the list:

Page 229 #2, 3, 5, 7, 8, 10, 11

Page 239 #1, 2, 3, 6, 9, 10, 11, 12

Remember, if you have trouble you need to contact me or see me before class. You have my email address, and you can comment on this post or tweet (@bgrasley) if you prefer. Thanks!