Permutations and Combinations

220

There are 12 different blizzard options. If you want to get three different kinds to share, how many ways is this possible?

278,256

Nathan has 34 jellybeans, in how many ways can he choose 5 to give to his friends?

40,320

Tracy wants to put her 8 figurines on the shelf. In how many ways can she order them?

362,880

Riley and the 8 other members of his family are going to a movie and are all sitting in the middle row. In how many orders can they sit?

60

Shawn and Alexis have 5 gender neutral names for their triplets picked out. In how many ways can they name their triples when they arrive?

72

Justin has 9 options for the last two periods of his daily schedule. In how many ways can he complete his schedule?

1716

There are 13 different types of doughnuts at the bakery, in how many ways can you select 7 different options?

105

There are 15 people who auditioned for the play. In how many ways can the two narrators be cast?

2024

There are 24 math problems on a quiz, in how many ways can you omit 3?

10,000

How many four digit locker combinations can be made from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9?

210

Castel and Joe are planning trips to three

countries this year. There are 7 countries

they would like to visit. One trip will be

one week long, another two days, and the

other two weeks

1,081,575

A group of 25 people are going to run a

race. The top 8 finishers advance to the

finals.

15

Carlos has homework assignments in six

subjects. He only has time to do four of

them

95,040

A coach must choose how to line up his five starters from a team of 12 players. How

many different ways can the coach choose the starters?

84

How many different committees of 3 people can be chosen to work on a special project

from a group of 9 people?

53,130

There are 25 people who work in an office together. Five of these people are selected

to go together to the same conference in Orlando, Florida. How many ways can they

choose this team of five people to go to the conference?

132

P(12,2)

24

P(4,4)

30,240

P(10,5)

840

P(7,4)

720

In the battle of the bands contest, in how many ways can the six participating bands perform?

13,800

In how man ways can a president, vice president, and secretary be randomly selected from a class of 25 students?

5040

How many four digit numbers do not contain the same digit more than once?

358800

A password consists of four different letters of the alphabet. How many different possible passwords are there?

3628800

An encyclopedia has ten volumes. In how many ways can the ten volumes be replaced on the shelf?

970200

How many ways are there to select a first-prize winner, a second-prize winner, and a third-prize winner from 100 different people who have entered a contest?

1037836800

Thirteen people on a softball team show up for a game.

How many ways are there to assign the 10 positions by selecting players from the 13 people who show up?

7920

Consider a group of 11 people.

How many ways are there to form a line of 4 people from the group?

6

How many strings are there that use each character in the set {a, b, c, d, e} exactly once (i.e.

permutations of {a,b,c,d,e}) and that start with an 'a' and end with an 'e'?

120

How many 3-digit numbers (with distinct digits) can we form using digits 0,1,2,3,4,5?

1320

There are 12 different blizzard options. If Karen, Joey, and Phil want to get three different kinds to share, how many ways is this possible?

96

Jordyn has 4 different jackets, 4 pairs of boots, and 6 different scarfs. In how many ways can she wear her outerwear?

108

A leadership team is to be picked at ACGC where one teacher from each department where there are 3 math teachers, 4 English teachers, 3 science teachers, and 3 social studies teachers. How many teams are possible?

6,375,600

There are 25 people who work in an office together. Five of these people are selected

to attend five different conferences. The first person selected will go to a conference in

Hawaii, the second will go to New York, the third will go to San Diego, the fourth will go to

Atlanta, and the fifth will go to Nashville. How many such selections are possible?

1260

At the grocery store, there are 4 kinds of meat to choose from and 10 kinds of vegetables. If you purchase 2 meats and 4 vegetables, how many different meals can you make?