Solve Me!
Mix-and-Match
Define
Identify the Parts
Who's going to win?
100
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 perform in a show? Is this a combination problem or a permutation problem?
165 ways. It's a combination problem.
100
Define permutation:
A way of arranging objects or values 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
If a team has won 2 games, but lost 8, what is the chance they will win their next game?
20%
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 if 100 students entered the raffle? Is this a combination problem or a permutation problem?
970200 ways. Permutation
200
Define combination:
A way of arranging objects or values where order does not matter.
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 what it means when "order matters"
Where each object or value holds a certain place value or order number 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
State the formulas used for combinations and permutations.
Combinations: C(n,r)=n!/(n-r)!r! Permutations: P(n,r)=n!/(n-r)!
400
Explain what it means when order does not matter:
Where an object or value can be in an un-ordered arrangement, for example where AB and BA is the same arrangement.
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
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
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
Define factorial and describe its symbol:
The result of multiplying a sequence of descending natural numbers. The symbol for it is "!". For example, 4 × 3 × 2 × 1 = 4!
500
Identify n and r in the following problem: How many possible phone numbers are there?
n=10 r=7
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?
The team most likely to win is Team D.
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