How many ways can we order a four topping pizza if there are seven toppings to chose from?
35
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
165
100
Choosing the starting five from a basketball team of 12.
Combination
100
Identify n and r in the following problem:
There are 35 boys trying out for football in the fall. The coach only has 20 spots to fill on the roster. How many ways can he fill the remaining spots?
n=35
r=20
100
Write the equation:
How many ways can 7 people be arranged around a circular table.
7! = 5,040
200
How many ways can you choose two jelly beans out of a bag of 15.
105
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 permutation problem?
Permutation
970,200
200
Choosing a President, Secretary, and Treasurer of the Math Club.
Permutation
200
Identify n and r in the following problem:
The school board has seven members, the board must have a chairperson, an assistant chairperson, and a secretary. How many different sets of these officers can be formed from this board?
n=7
r=3
200
Write the Equation:
Verizon offers 6 phones, 12 texting plans, 4 calling plans, and 3 data plans.
How many different plans can you make if you choose 1 phone, 1 calling plan, 1 data plan, and one texting plan.
(6)(12)(4)(3) = 864
300
How many ways can 5 different books be arranged on a shelf.
5! = 120
300
A) When does order matter?
B) When does order not matter?
A) Permutations
B) Combinations
300
Choosing 3 pizza toppings from the 12 topping available
Combination
300
Identify n and r the following
Ten band directors at a summer band camp are planning to give a performance. One of the pieces they want to play calls for a Flute, an oboe, a bassoon, and a clarinet. Each of the band directors can play all four instruments. How many different quartets can they have
n=10
r=4
300
Write the equation:
How many different ways can a gold, silver, and bronze medal be awarded among 15 competitors.
n!/(n-r)! = 15!/(15-4)!
32,760
400
If there are 40 NASCAR drivers at Bristol Motor Speedway. How many different lineups can be made for the top 5.
78,960,960
400
15 technicians and 11 chemists work in a research lab. How many different ways can they form a 5 person safety committee.
65,780
400
Choosing a first place and runner up in a contest.
Permutation
400
Identify n and r in the following problem:
How many ways can you deal a five card hand from a standard deck?
n=52
r=5
400
Write the equation:
A set of 12 encyclopedias is arranged on a shelf. How many incorrect arrangements are possible?
12! - 1
479,001,599
500
How many different 4 digit pins can be made for your debit card.
10,000
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
500
Choosing a dinner consisting of one meat and two vegetables from 3 types of meat and 6 different vegetables.
Combination
500
Identify n and r in the following problem:
How many possible phone numbers (including area code) are there?
n=10
r=7
500
Solve this problem:
Ms. Bagwell has a lock with a four digit combination. She does not like the numbers 6,0,or 1 and will not use them in her combination. How many different 4 digit combinations can she choose from if her combination must be an even number and must start with 7.