16.a Combinations

Question 1

What is the difference between combinations and permutations?

Answer 1

In combination questions it does not matter in which order a task is completed.

In permutation questions the order in which a task is completed matters.

Question 2

What do combination questions ask?

Answer 2

To count the number of possible ways in which a task can be performed when the order in which the task is accomplished does NOT matter.

Question 3

What problem is this, permutation or combination?

“There are 4 different types of coffee to choose from, if we must choose two different coffees to drink, how many different coffee selections are possible that morning?”

Answer 3

Combination,

Order does NOT matter

Question 4

What problem is this, permutation or combination?

“There are 4 different types of coffee to choose from, if we must choose two different coffees to drink and the order in which you drink them, how many different coffee selections are possible that morning?”

Answer 4

Permutation

Order MATTERS

Question 5

What problem is this, permutation or combination?

“A tycoon has 10 different sports cars in his garage. How many possible ways are there for him to arrange three of the cars in a line?”

Answer 5

PERMUTATION

In this case we are lining up the cars, so order does matter.

Imagine, Mustang-Corvette-Ferrari,

that differs from:
Corvette-Ferrari-Mustang

Question 6

What problem is this, permutation or combination?

“At an airport gate, how many different groups of three people could be chosen from a standby list of eight people?”

Answer 6

Combination problem

Order does NOT matter

Question 7

What problem is this, permutation or combination?

“A club has 12 members, the officers in the club are President, Secretary and Treasurer. In how many ways could these three positions be filled from the membership?”

Answer 7

PERMUTATION

Order does matter.
eg. choosing Karl as president, Laura as secretary and Rory as treasurer, is different to: Laura as president, Rory as secretary and Karl as treasurer

Question 8

What is the basic Combination Formula?

Answer 8

Question 9

Explain this

Answer 9

n = number of objects from which we will choose
k = the number of objects we will actually choose

this formula applies to situations known as “n choose k”

Question 10

Fill in this formula if you have to select 5 items from a pool of 10 items?

Answer 10

5 items from a pool of 10
“10, choose 5” (“n choose k”)

n = 10
k = 5

Question 11

What is the shortcut “box and fill” method?

Answer 11

Question 12

What is a “handshake” question?

Answer 12

Any counting question that asks us to determine the number of ways to connect any two members of a group while also meeting any restrictions that may exist

Question 13

Solve this:

Answer 13

Question 14

What is the handshake formula?

Answer 14

where:

n = number of entities
k = number of entities each entity is connected to

Question 15

Solve:

Answer 15

Question 16

If each entity is only connected to a portion of the total entities, what method must you use?

Answer 16

The handshake formula

Question 17

Solve:

Answer 17

Question 18

Solve:

Answer 18

Question 19

What can you do when dealing with very large numbers?

Answer 19

Use the combination equivalent formula

Question 20

What is the Combination Equivalent Formula?

Answer 20

Question 21

Solve:

Answer 21

Question 22

Solve:

Answer 22