Show:
Solve Me!
Mix-and-Match
Define
Identify the Parts
Pascal's Triangle
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 preform in a show/ Would this be a combination problem or a permutaion problem?
Combination
100
Define permutation:
What is a way of arranging in an ordered fashion of objects or values where order matters.
100

Identify n and k 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 k=20

100

What are the numbers in the 3rd row of Pascal's Triangle?

1,3,3,1

200

Compute C(16,10)

8,008

16!/(6!10!)  or (16*15*14*13*12*11*10*9*8*7)/10!

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:
What is a way of arranging objects or values where order does not matter.
200

Identify n and k 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 k=3

200

If I wanted to expand the binomial (a+b)25, what row of Pascal's triangle would give me the coefficients?

The 25th row.

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:

What is where each object or value holds a certain place value in an arrangement.

300

Identify n and k 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 k=4

300

C(7,2) will tell me.....

(there are 3 different possible answers!)

a) the number of ways to choose 2 items out of 7 (combination)

or b)the value in the 7th row, 2nd entry on Pascal's triangle

or c) the coefficient on the a5b2 term for (a+b)7

400
How many ways can you deal a five card hand from a standard deck if order doesn't matter?
2,598,960
400

What are two ways to calculate a permutation?

Using P(n,k): 

Multiplication principle:   n*(n-1)*(n-2)*....  for k terms

or n!/(n-k)!

400
Explain order does not matter:
What is where an object or value can is in an un-ordered arrangement where AB=BA is the same arrangment.
400

Identify n and k in the following problem: How many ways can you deal a five card hand from a standard deck?

n=52 k=5

400
Fill in the blanks: 


(a+b)4 = 1a4 + 4a3b+ ____a2b2 + 4_____+ 1_____

In order: 

6  (can be found out by doing C(4,2) or 4th row 2nd entry on PT)

ab3

b4

500

There are 53 band students going on a fieldtrip, how many ways can the director choose two student leaders for the bus ride?

1,378

500
A New Hampshire driver's license has an ID number that has 2 digits, followed by 3 letters, followed by 5 digits. How many different ID numbers are possible?

1.76x1011  or 175,760,000,000 (assuming all letters and numbers can be repeated.) 

500

Define what 6! means.

Multiply all integer values starting at 6 and going down to 1. 

6*5*4*3*2*1

500

Identify n and k in the following problem:

The counseling department has to make appointments for planning meetings.  Mr. Loomis has 125 students, and he can make an appointment every half hour between 8 and 2pm. 

n= 125   k=12

500

How can you calculate C(100, 3), and where is that same answer located on Pascal's triangle?

C(100,3) = (100*99*98)/3! 

or 100!/(3!97!)


The same value will be found in row 11, entry 3.