For this problem, since the order of the vases matters (red blue yellow is different than blue red yellow), we're dealing with permutations.

With  selections made from  potential options, the total number of possible permutations(order matters) is:

Since the order in which Lisa layers up matters, we're dealing with permutations.

With  selections made from  potential options, the total number of possible permutations is:

For her shirts:

For her socks:

Her total ensemble options  is the product of these two results

With  selections made from  potential options, the total number of possible permutations(order matters) is:

Quantity A:

Quantity B:

Quantity A is greater.

For this problem, order matters! Wearing a particular blouse on Friday is not the same as wearing it on Sunday. So that means that this problem will be dealing with permutations.

With  selections made from  potential options, the total number of possible permutations(order matters) is:

What we'll do is calculate the number of permutations for her blouses, skirts, and shoes seperately (determining how the Friday/Saturday/Sunday blouses/skirts/shoes could be decided), and then multiply these values.

Blouses:

Skirts:

Shoes:

Thus the number of potential outfit assignments is

Step 1: We need to identify how many seats there are on the bench. We have 5 names, so 5 seats.

Step 2: When 1 person sits in seat 1, he/she cannot sit in the next set, and so on.

Step 3: Let's work out the math...

Seat 1- 5 people can sit
Seat 2- 4 people can sit
Seat 3- 3 people can sit
Seat 4/5-2/1 people/person can sit 

Total possibilities=. We can also say that 

This is a permutation. A permutation is an arrangement of objects in a specific order.

The formula for permutations is:

This is written as 

There are  possible groups of 3.

This is a permutation. A permutation is an arrangement of objects in a specific order.

The formula for permutations is:

This is written as 

 represents the number of permutations of 23 things taken 3 at a time.

 is asking to find the permutation of seven items when you want to choose five. When dealing with permutations, order matters.

A permutation is an arrangement of objects in a specific order.

The formula for permutations is:

This is written as 

 is asking to find the permutation of four items when you want to choose all four. When dealing with permutations, order matters.

A permutation is an arrangement of objects in a specific order.

The formula for permutations in this case will be,

 or  factorial.

Step 1: A handshake MUST ALWAYS be between TWO people.

Step 2: Break down each person and who they can shake hands with:

Person  can shake hands with: . 
Person  can shake hands with: 
Person  can shake hands with: 
Person  can shake hands with: 
Person  can shake hands with: 
Person  can shake hands with: 
Person  can shake hands with: 
Person  can shake hands with: 
Person  can shake hands with: 
Person  can shake hands with: 
Person  already shook everybody's hand..

Step 3: Count how many handshakes each person can make:

Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  time.
Person  already shook everybody's hand.

Step 4: Add up the number of times each person shook hands:



There were  handshakes made between these  people.