Permutations and Combinations Lesson 3

Intro:  I would play this movie to catch the attention:

Review of previously learned material consists of the following problems:  ***You will have to decide how many people are lining up and how many are men/women together as a class**

1)  In the video how many different ways can the people line up with
a) no restrictions
b) The men behind the women.
c) the women standing together
d) the women aren't standing together

2) Later, 3 cab drivers pull up simultaneously.  Determine the number of distinct permutations you could have if each person travels alone.

3) The next day, 2 cabs pull up and there are 30 different ways they can drive the number of people present with one person in each cab.  Determine the number of people waiting in line.

4) How many different possible values of r could there be if we were calculating 8Pr?

Go through the questions, after giving some time for the students to work on them cooperatively.

Body:

 

A thief was trying to break into a keypad and he sprayed it with Luminol.  A chemical which brightens when it comes into contact with the oils left by a finger.  He noticed that there were a fingerprint on the number 2 and 7, and two fingerprints on the number 4.  How many different possibilities are there for the code to the safe?

Let students work and struggle through, and lead them towards the identity of:

Organizing a objects where there are n repetitions of one object, there are a!/n! distinct permutations.

 

Questions:

1) Hertz Rental Cars has 3 identical SUVs, 5 identical cars, and 6 identical trucks.  Determine the number of arrangements Hertz can have using all their vehicles.

2) How many PIN numbers can you create if they must be 5 digits long where 3 digits must be the same?

3) Create a scenario where you would calculate 8!/(3!2!) to arrive at the solution.