Permutation and Combination

Seating 5 men and 5 women alternately in a row, beginning with a woman.

Farmington High is planning its academic festival. All math classes will send 2 representatives to compete in the math bowl. How many different groups of students can be chosen from a class of 16 students?

Choosing 3 side-dishes from a menu that offers 6 vegetable side-dishes and 4 starches if you want at least one of each.

Introducing the 5 starting players on the Blue Devil’s basketball team at the beginning of the next basketball game.

An arrangement of the letters in the word rhombus.

From a group of 10 men and 12 women, how many committees of 5 men and 6 women can be formed?

Seating 8 students in 8 seats in the front row of the school auditorium.

A photographer is taking pictures of a bride and groom and their 6 attendants. If she takes photographs of 3 people in a group, how many different groups can she photograph?

How many hockey teams of 6 players can be formed from 14 players without regard to position played?

Selecting 3 desserts from 10 possible choices displayed on the dessert cart at a restaurant.

Selecting 2 of 8 possible different brands of orange juice at the store.

Choosing the first, second, and third-place finishers in a race with 10 competitors

electing a 4-person bobsled team, if one of the team members must be from a group of 9 football players and the other 3 may be from a group of 8 other athletes.

You are asked to list, in order of preference, the 5 best movies you have seen this year. If you saw 7 movies during the year, calculate how many ways your list can be arranged.

An arrangement of the letters in the word isosceles.

Electing 4 candidates to a municipal planning board from a field of 7 candidates.

Forming a 4-person sales team from a group of 12 salesmen and 8 saleswomen, if you want at most 2 women on the team.

Placing a red rose bush, a yellow rose bush, a white rose bush, and a pink rose busy in a row in a planter.

In how many ways can you pick 5 cards if you must choose a Queen, then a King and, then 3 other cards if every card is drawn one at a time?

Selecting 2 orange tabbies from 9 kittens at an animal rescue shelter.

Checking out 4 library books from a list of 8 books for a research paper.

A school librarian would like to buy subscriptions to 7 new magazines. Her budget however, will allow her to buy only 4 new subscriptions. How many different groups of 4 magazines can she choose from the 7 magazines?

Arranging 4 charms from 6 possible, on a bracelet that has a clasp, a front, and a back.

Making a 5-sided polygon by choosing any of 5 of 11 points located on a circle to be the vertices.

A track race consists of 9 runners. In how many ways can the podium of the top 3 runners be ordered?

Choosing 5 movies to rent if you want at least 2 Westerns. The store has 8 Westerns and 12 Science Fiction films.

An airline is hiring 5 flight attendants. If 8 people apply for the job, how many different groups of 5 attendants can the airline hire?

From a standard deck of 52 cards, in how many ways can 7 cards be drawn?

Your school newspaper has an editor-in-chief and an assistant editor-in-chief. The staff of the newspaper has 12 students. In how many ways can students be chosen for these two positions?