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
100
Define permutation:
Refers to the different possible arrangements of a set of objects and where order matters.
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
20 politicians are running for the offices of president, secretary and treasurer. In how many ways can these offices be filled?
6840
200
Compute C(16,10)
12,870
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
200
Define combination:
The number of ways of selecting from a set when order is not important.
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
If a team has a history of winning 70% of their games and there are 20 games in a season, how many games should they win this season?
14 games
300
Solve P(8,2)
56
300
A) When does order matter?
B) When does order not matter?
A) Permutations
B) Combinations
300
Explain order matters:
Is where each object or value holds a certain place value in an arrangement.
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
The Bobcats have a record of (10, 15) and the Gators have a record of winning 45% of their games. Who is likely to win when the Gators and Bobcats play each other?
The Gators should win.
400
How many ways can you deal a five card hand from a standard deck if order doesn't matter?
2,598,960
400
In a 10-item Mathematics problem-solving test, how many ways can you select 5 problems to solve?
252
400
Explain order does not matter:
Is where an object or value in un-ordered arrangement is the same arrangment. Such as AB=BA.
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
The Huskies have a record of (17, 9) and the Bears have a record of winning 65% of their games. Who is likely to win when the Huskies and Bears play each other?
The Huskies are more likely to win.
500
If there are 12 teams in a basketball tournament and each team must play every other team in the elimination, how many elimination games will there be?
66
500
In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors?
350
500
Define probability:
What is a way of expressing knowledge or belief that an event will occur or has occurred.
500
Identify n and r in the following problem:
How many 4-digit numbers can be formed from the digits 1,3,5,6,8, and 9 if no repetition is not allowed?
n=6
r=4
500
There are 4 teams in tournament. Team A wins 50% of their games. Team B has a record of (12, 10). Team C loses 40% of their games. Team D has a record of winning 2/3 of their games. Which team is has the highest probability of winning?