Permutations Combinations

Question 1

Counting principle

Answer 1

If one event can occur in m ways and another in n ways then the number that both can occur is (mn)
For three
(Mn*p)

Question 2

If you are buying a pizza, 3 choices for crust, 4 cheeses, 5 meat toppings, and 8 vegetables. How many different pizzas can be made with one of each topping

Answer 2

345*8= 480

Question 3

Permutation

Answer 3

An ORDERING of n objects

Question 4

How can you find the number of permutations

Answer 4

Use factorial

Question 5

Factorial

Answer 5

3!= 321

Question 6

Eight teams are competing, how many different ways can the baseball team finish the competition

Answer 6

8765432*1

Or 8!

Question 7

Permutations of objects taken at a time

Equation

Answer 7

Objects-n
Taken at a time-r
nPr

First total then taken

Question 8

You have 6 homework assignments to complete but you can only complete 4. How many orders can you complete them

Answer 8

6P4

Question 9

Permutations with repetition

Answer 9

Number of distinguishable permutations of N objects where one object is repeated S times another S2 times and so on
N!
S! + S2!….

Question 10

Find the number of distinguishable permutations of the letters in even

Answer 10

N= 4 letters
E repeats twice
4!
2!

Question 11

Combination

Answer 11

Combinations of R objects taken from a group of N distinct objects nCr, order doesn’t matter

Question 12

If you are picking 7 books from a stack of 32 and the order doesn’t matter, how many different seven book groups are possible

Answer 12

32C7

Question 13

When finding the number of ways both an event A and event B can occur, you need to —- their combinations

Answer 13

Multiply

Question 14

When finding the number of ways that an event A or event B can occur, you need to —- their combinations

Answer 14

Add

Question 15

When problems include statements like at least or at most , it is sometimes easier to —– combinations you do not want from the total

Answer 15

Subtract

Question 16

There are 12 comedies, 8 action, 7 drama, 5 suspense, 9 family. You want exactly 2 comedies and 3 family. How many different combos

Answer 16

(12C2) * (9C3)

Question 17

Pascal triangle 
0 degree
1 degree
2 degree
3 degree
Coefficients for each

Answer 17

1
1 1
1 2 1
1 3 3 1

Question 18

Pascal’s triangle

Answer 18

The first and last numbers in each row are 1. Every number other than 1 is the sum of the closest two numbers in the row above it

Question 19

Expanding binomial

Answer 19

Use Pascal’s triangle for coefficients
Then degrees it’s the highest degree and 0 , then the highest decreases by one each time and 0 increases by one each time

Question 20

Find the coefficient in an expansion equation

Answer 20

nCr * a^n-r * b^r 
N is degree of expansion 
R- found when plugged in 
a is the first part of binomial
B is second part

Question 21

For expanding binomial when it’s a minus what’s the pattern

Answer 21

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