Permutations and Combinations

Pg 1.2 : How many different ways can you line up 5 skittles, each a different color?Pg 1.3 : How many different ways can you line up just 3 of the 5 skittles?

Permutations: order or arrangement matters

ABCD is not the same as BACD even though they have the exact same elements.

nPr = n!/(n-r)!

You may not use an element more than once.

Pg 1.4- In a race with 8 runners, how many different top 3 finishes are possible?

How many different ways can you choose 5 of the 5 skittles where order doesn’t matter?

Pg 1.5 : How many different ways can choose 3 of the skittles and by the way, the order doesn’t matter – RPY is the same as PRY

Combinations: order doesn’t matter

ABCD is the same as BACD which is the same as CABD etc…

Page 1.6- The betting slips of NJ’s pick-6 Loto game offer a field of numbers from 1 to 49. Each bettor chooses any 6 of them. You win

the grand prize if you six numbers match those randomly chosen. How many different selections are possible?

The r! cancels out all the repeats of the same set in a different order

nCr = n!/r!(n-r)!Pg 1.7 Answer 7C3; 10C7;

what does 6C2 mean?

WAYS TO COUNTPermutations: permutations of n objects taken r at a time

where the order does matter.Combinations: combinations of n objects taken r at a time

where the order doesn’t matter.Selections: filling spots with or without repeats.

Multiplying possible selections for each spot.

Pg 2.1- Using the pattern of letters and numbers, how many different license plates are possible for this style of Utah plate?

Selection: how many possibilities for each element all multiplied together. One selection is independent of the next selection.

B1) Motorcycle plates have 5 figures but the first 2 are letters while the last 3 are digits. How many possible different plates are there for Motorcycles?

Pg 2.2- The access code for an ATM is 4 digits. How many different access codes are possible?

Selection: how many possibilities for each element all multiplied together. One selection is independent of the next selection.

B2) Your bank requires an access code of 4 places where you can use a digit or 2 special symbols * or #. How many more possible codes does this allow versus just using digits?

Pg 2.3- The login code for an email site is 5 characters and can be letters or digits in any order. How many possible login codes are

there?

B3) The login code for an email site is 5 characters and can be letters or digits in any order but you can only use a letter or digit once. How many possible login codes are there?

B4)- Practice on notes:

1. 4! =

2. 6! =

3. 5!/3! =

4. 10!/9! =

5. 0! =

Practice:

3.1- You just downloaded 5 new albums to your iPod, and are eager to listen to them. How many different orders can you play the albums in?

B5) You take your iPod to the mountains and select a playlist of your 10 favorite albums to be played in random order. You’ll be there long enough to hear 5 of them. How many different orders of albums could you get to listen to?

C)- Practice on notes: A county legislature consists of 13 elected reps., 5 Dems and 8 Reps. They’re

setting up a 4 person committee to study a new proposal to build a new library. How many different committees could be formed if the group will consist of:

1- 4 Rep.

2- 4 Dem.

3- 2 Dem & 2 Rep.

4- 3 Rep & 1 Dem.

5- 2 or 3 Rep. the rest Dem

Spot 1 Spot 2 Spot 3 Spot 4

Practice: A video rental store is going out of business and is offering “DVD grab bags”. You can buy a bag of 6 DVD’s made from a randomly selected group of 15 recently popular movies. The group of 15

included 4 comedies, 8 dramas and 3 animated features. What is the probability that your grab bag contains

Pg 4.1 & D1- 2 comedies, 3 dramas and 1 animated flick?Pg 4.2 & D2- nothing but dramasPg 4.3 & D3- 3 of the comedies and 3 dramas

Spot 1 Spot 2 Spot 3 Spot 4 Spot 5 Spot 6