Combinations and Permutations!

Solve Me!

100

How many ways can we order a four topping pizza if there are seven toppings to chose from?

35

200

Compute C(16,10)

12,870

300

Solve P(8,2)

56

400

How many ways can you deal a five card hand from a standard deck if order doesn't matter?

2,598,960

500

There are 53 band students going on a fieldtrip, how many ways can the teacher put them in groups of two for the bus ride?

1,378

Mix-and-Match

100

There are 11 clowns in a circus, how many ways can you group the clowns if only three preform in a show/ Would this be a combination problem or a permutaion problem?

Combination

200

There is a school raffle this week, the first prize is a coffee mug, the second prize is a car, and the third prize is a candy bar. How many ways can you hand out the prizes in 100 students entered the raffle? Would this be a combination problem or a permutaion problem?

Permutation

300

How many ways can you select a sundae that consists of 1 ice cream and 2 toppings. Your ice cream choices are vanilla, chocolate, peach and strawberry Your topping choices are chocolate sauce, caramel sauce, cherries, strawberries and nuts?

40

400

A pollster must randomly select 3 of 12 available people. How many different groups of 3 are possible?

220

500

To open your locker, you must dial a sequence of three numbers called the lock’s combination. Given that there are 40 numbers on a lock, how many different locker combinations are there?

59,280

Counting Principle

100

You go to a I-Hop to get some breakfast. The menu says pancakes, waffles, or omletes. And for a drink, you can choose coffee, juice, hot chocolate or tea. How many different choices of food and drink do you have?

3 x 4 = 12

200

STUCO is electing new officers. There are 2 candidates for president, 3 candidates for vice-president, and 4 candidates for secretary, and 2 candidates for treasurer. How many different combinations of officers are possible?

2x3x4x2 = 48

300

You toss a quarter 4 times. How many different outcomes are there?

2x2x2x2 = 16

400

When you get ready to get dressed for school, you open your closet to find you have the following choices: a red, blue, or white shirt; jeans, shorts or sweatpants; tennis shoes or sandals. How many different outfits could be made with these choices?

3x3x2 = 18

500

In Canada, a postal code consists of a letter, a digit, a letter, a digit, a letter, and a digit. How many different postal codes are possible in Canada?

26x10x26x10x26x10 = 17,576,000

Permutations

100

A computer operator must select 4 jobs from among 10 available jobs waiting to be completed. How many different sequences are possible?

5040

200

A union must elect 4 officers from 16 available candidates. How many different slates are possible if 1 candidate is nominated for each office?

43,680

300

 A football team has 6 basic plays. How many arrangements of three different plays could be called?

120

400

There are 7 empty seats on a bus and four people enter. In how many different ways can they be seated?

840

500

There are 8 horses in a race. In how many ways can the win, place, and show horses be selected?

336

Combinations

100

How many 2-member committees can be chosen from 7 people?

21

200

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

3003

300

You want to buy 3 hats but there are 9 hats that you like. How many possible combinations of the 3 hats can you choose?

84

400

McDonalds is hiring 4 new employees. If 7 people apply for the job, how many different groups of 4 can McDonalds hire?

35

500

There are 30 members in FFA. Two people are selected to go to the national conference. In how many ways can the 2 members be selected?

435