Permutations Combinations Flashcards Preview

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Flashcards in Permutations Combinations Deck (21)
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1
Q

Counting principle

A

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

2
Q

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

A

345*8= 480

3
Q

Permutation

A

An ORDERING of n objects

4
Q

How can you find the number of permutations

A

Use factorial

5
Q

Factorial

A

3!= 321

6
Q

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

A

8765432*1

Or 8!

7
Q

Permutations of objects taken at a time

Equation

A

Objects-n
Taken at a time-r
nPr

First total then taken

8
Q

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

A

6P4

9
Q

Permutations with repetition

A

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

10
Q

Find the number of distinguishable permutations of the letters in even

A

N= 4 letters
E repeats twice
4!
2!

11
Q

Combination

A

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

12
Q

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

A

32C7

13
Q

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

A

Multiply

14
Q

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

A

Add

15
Q

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

A

Subtract

16
Q

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

A

(12C2) * (9C3)

17
Q
Pascal triangle 
0 degree
1 degree
2 degree
3 degree
Coefficients for each
A

1
1 1
1 2 1
1 3 3 1

18
Q

Pascal’s triangle

A

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
Q

Expanding binomial

A

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
Q

Find the coefficient in an expansion equation

A
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
Q

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

A

-+-+-+….