Flashcards in Permutations Combinations Deck (21):

1

## Counting principle

###
If one event can occur in m ways and another in n ways then the number that both can occur is (m*n)

For three

(M*n*p)

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

### 3*4*5*8= 480

3

## Permutation

### An ORDERING of n objects

4

## How can you find the number of permutations

### Use factorial

5

## Factorial

### 3!= 3*2*1

6

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

###
8*7*6*5*4*3*2*1

Or 8!

7

##
Permutations of objects taken at a time

Equation

###
Objects-n

Taken at a time-r

nPr

First total then taken

8

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

### 6P4

9

## Permutations with repetition

###
Number of distinguishable permutations of N objects where one object is repeated S times another S2 times and so on

N!

S! + S2!....

10

## Find the number of distinguishable permutations of the letters in even

###
N= 4 letters

E repeats twice

4!

2!

11

## Combination

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

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

### 32C7

13

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

### Multiply

14

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

### Add

15

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

### Subtract

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

### (12C2) * (9C3)

17

##
Pascal triangle

0 degree

1 degree

2 degree

3 degree

Coefficients for each

###
1

1 1

1 2 1

1 3 3 1

18

## Pascal's triangle

### 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

19

## Expanding binomial

###
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

20

## Find the coefficient in an expansion equation

###
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

21