This lesson is about counting problems using the Fundamental Counting Priniciple.

1. Skill19 Counting Problems
Pages 112 – 115 from the book
The problems from this section depend on one main principle. That is to multiply
Numbers of ways to make decisions. I call these slot problems. That is to say, just make
a blank for each decision and put the numbers in the blanks and then multiply.
This can be a very easy question that you may very well see on the GED Test.
Example. If you have 4 pair of pants that match 3 shirts, how many outfits can you
make? ____ X ______ which would be 4 X 3 or 12 outfits. Easy right?

2. Think of the problem this way: Draw out a slot for all six books. In the first blank, put
6 because there are 6 ways to pick the first book. In the second slot, put 5 because there
only 5 books left to choose from for the second book. In the third slot, put 4. In the next
slot put 3, then 2, then 1 (there is only one way to choose the last book.)

3. Look at these arrangement problems with the answers and work shown at the bottom. See
The next slide for some explanation.

4. Start by drawing three blanks, one for each office to be elected.
____ X ______ X ______ 10 X 9 X 8 Because there are 10 people to select
from for the first office. That leaves only 9 left to choose from for the second office.
Then there are only 8 ways to pick the secretary, the third office.
Multiply to get 720.
Draw four blanks for the four offices. 10 ways to pick the first office, 9 people left
to pick the second, then 8, then 7. So, 10 X 9 X 8 X 7 or 5040
Try the other problems on page 113 and look at the work for each below the
answers below the last problem.

5. Look at these problems from page 115. They are basically the same except
that in the first version, you can use all the letters -- repetitions are allowed.
That means you keep 26 ways for each slot.
In the second version, repetitions are not allowed. That means that you cannot
reuse any letter one it is used so reduce the number of ways by one for each slot.
The key difference in the two problems is whether or not repetition is allowed.
If it is, don’t reduce the number of ways for the following blanks.
If it is not allowed, reduce the number of ways for the following blanks by one each
blank.
Try the other problems on page 115. They are worked out for you.