Exam 31: Counting Rules

There are 10 finalists at a national dog show.How many different orders of finishing can there be for all the 10 finalists?

There are 47 contestants at a national dog show.How many different ways can contestants fill the first place,second place,and third place positions?

At the International Pancakes Hut,there are 4 different ways to have an egg cooked,7 different choices of pancakes,5 different types of syrups and 8 different beverages.How many different ways are there to order an egg,a pancake with a choice of syrup and a beverage?

Seven passengers are on a waiting list for an overbooked flight.As a result of cancellations,3 seats become available.How many different ways can those 3 available seats be filled regardless of the order?

There are only 4 empty rooms available in a student dormitory for eleven new freshmen.Each room is considered unique so that it matters who is being assigned to which room.How many different ways can those 4 empty rooms be filled,one student per room?

Twelve students in a Business Statistics class are to be formed into three teams of four.How many different ways can this be done?

A debate team of 4 is to be chosen from a class of 35.There are two twin brothers in the class.How many possible ways can the team be formed which will not include any of the twin brothers?

Four freshmen are to be assigned to eleven empty rooms in a student dormitory.All the rooms are considered as homogenous so that it does not matter who is being assigned to which room.How many different ways can those 4 freshmen be assigned?

A debate team of 4 is to be chosen from a class of 35.There are two twin brothers in the class.How many possible ways can the team be formed which will include both of the twin brothers?

A high school debate team of 4 is to be chosen from a class of 35.How many possible ways can the team be formed?

There are only 4 empty rooms available in a student dormitory for eleven new freshmen.All the rooms are considered as homogenous so that it does not matter who is being assigned to which room.How many different ways can those 4 empty rooms be filled,one student per room?

An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men.How many different ways can this team of 5 be formed?

Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory.Each room is considered unique so that it matters who is being assigned to which room.How many different ways can those eleven freshmen be allocated?

A debate team of 4 is to be chosen from a class of 35.There are two twin brothers in the class.How many possible ways can the team be formed which will include only one of the twin brothers?