Permutations Combinations Flashcards Preview

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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

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

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