16.c Permutations

Question 1

In a permutation, the ___________ matters

Answer 1

In a permutation, the ORDER matters

Question 2

How many permutations are there of ABC?

Answer 2

Question 3

Explain how this is a permutation question

Answer 3

Question 4

What is the “Basic Permutation Formula”?

Answer 4

n = number of objects from which a choice can be made
k = number of objects that are to be chosen

Question 5

Solve this question using the formula

Answer 5

Question 6

Solve this question using the “box-and-fill”

Answer 6

Question 7

How do you solve a permutation problem using the box-and-fill method?

Answer 7

Let each box represent a specific choice that must be made.
Multiply the numbers in each box.

Question 8

In permutation problems count only the number of _________________ permutations

Answer 8

In permutation problems count only the number of DISTINGUISHABLE permutations

Question 9

How many permutations are there of: [S, S, S, S, S]?

Answer 9

None!
[S, S, S, S, S]
The entire list has the same letter, thus even if put in another order it would not be distinguishable.

Question 10

How would you solve a permutation problem for the list: [A, A, B, B] ?

Answer 10

[ A, A, B, B ]

Question 11

What is the equation used to solve permutation problems that contains identical/ indistinguishable items?

Answer 11

N = total number of objects
r = frequency of each indistinguishable object

Question 12

How would you solve a permutation problem for the list: [G, S, P, P, T] ?

Answer 12

Question 13

What are “pathway questions”?

Answer 13

Need us to determine the total number of different paths one can take to travel from starting point to some destination

Question 14

What is a “checkpoint”

Answer 14

While traveling from a starting point to a destination, a point that travelers MUST pass through

Question 15

How would you tackle this?
Explain the steps.

Answer 15

Look in-between the checkpoint how many ways there are.
= Multiply these!

Question 16

Solve:

Answer 16

Calculate for the top and bottom, and then add them

Question 17

Conceptually, how would you solve this:

Answer 17

Understand that in whatever way you travel, you have to go South 4 times, and East 3 times.

So, the problem becomes: “In how many ways can we arrange 4 S’ and 3 E’s ?

Question 18

Solve this

Answer 18

[ S, S, S, S, E, E, E ]

Question 19

Conceptually, explain how you would solve this:

Answer 19

Find the number of ways you can travel from Y to C,
Find the number of ways you can travel from C to X,

Multiply the two values for TOTAL

Question 20

How would you solve this?

Answer 20

Exact same way as solving a two-dimensional problem,
Just add ANOTHER length

Question 21

What is the circle permutation formula?

Answer 21

Question 22

Solve:

Answer 22

k = 6

Question 23

Solve:

Answer 23

Question 24

What should you do if some items have to be together in a permutation problem (eg. always stand next to each other)?

Answer 24

LINK the items together!

Example: If A, J, S, M and T have to be arranged in a line, how many ways can this be done if J and S always have to stand together?
= Just consider J and S, a single item! LINK them!

HOWEVER, also watch out as there are two ways of linking them,
either JS, or SJ.

You have to account for this

Question 25

What is the formula for items that are linked together?

Answer 25

T = total # of items g = # of items that must be together

Question 26

Solve:

Answer 26

Question 27

How would you solve a question where it asks you that some items can NOT be together in a permutation problem?

Answer 27

Remember "Collectively Exhaustive Events of ways items not together = # of all arrangements - # of arrangements together

Question 28

Explain how you would solve this

Answer 28

of ways items not together = # of all arrangements - # of arrangements together

Question 29

Solve:

Answer 29