http://www.ck12.org Chapter 12. Discrete Math
Adecision chartis a sequence of numbers that multiply together where each number represents the number of
possible options for that slot.
Guided Practice
- There are 20 hockey players on a pro NHL team, two of which are goalies. In how many different ways can 5
skaters and 1 goalie be on the ice at the same time? - In how many different ways could you score a 70% on a 10 question test where each question is weighted equally
and is either right or wrong? - How many different 4 digit ATM passwords are there? Assume you can repeat digits.
Answers: - The question asks for how many on the ice, implying that order does not matter. This is combination problem
with two combinations. You need to choose 1 goalie out of a possible of 2 and choose 5 skaters out of a possible 18.(
2
1
)( 18
5
)
= 2 ·5!18!·13!= 17136
- The order of the questions you got right does not matter, so this is a combination problem.(
10
7
)
=7!3!10!= 120
- Order does matter. There are 10 digits and repetition is allowed. You can use a decision chart for each of the four
options.
10 · 10 · 10 · 10 = 10 , 000
Practice
Simplify each of the following expressions so that they do not have a factorial symbol.
1.7!3!
2.105!5!110!
3.52!49!
- In how many ways can you choose 3 objects from a set of 9 objects?
- In how many ways can you choose and arrange 4 objects from a set of 15 objects?
First, state whether each problem is apermutation/decision chartproblem or acombinationproblem. Then, solve. - Suppose you need to choose a new combination for your combination lock. You have to choose 3 numbers, each
different and between 0 and 40. How many combinations are there? - You just won a contest where you can choose 2 friends to go with you to a concert. You have five friends who are
available and want to go. In how many ways can you choose the friends? - You want to construct a 3 digit number from the digits 4, 6, 8, 9. How many possible numbers are there?
- There are 12 workshops at a conference and Sam has to choose 3 to attend. In how many ways can he choose the
3 to attend? - 9 girls and 5 boys are finalists in a contest. In how many ways can 1st, 2nd, and 3rdplace winners be chosen?
- For the special at a restaurant you can choose 3 different items from the 10 item menu. How many different
combinations of meals could you get?