U4

Question 1

How to use the fundamental counting principle

Answer 1

multiply the number of choices for each stage together

Question 2

Before finding the number of options for other stages what do you HAVE to do first

Answer 2

Consider any restrictions for a particular stage

Question 3

Does order matter in permutations

Answer 3

YES

Question 4

What is the notation for a permutation and what do the variables represent

Answer 4

(sub n)P(sub r)

n= total # of objects 
r= # of objects chosen

Question 5

What is the purpose of a factorial

Answer 5

A short way to write a multiplication statement of descending WHOLE numbers

Question 6

What is “n” an element of

Answer 6

Whole numbers

Question 7

How do you write (4)(3)(2)(1) as a factorial

Answer 7

4!

Question 8

Is arranging letters of a word a perm or comb

Answer 8

Perm

Question 9

Is arranging people in a line a perm or comb

Answer 9

Perm

Question 10

How do you solve

(sub n) P (sub 2)

Answer 10

1) plug into perm formula

2) expand n! on the top to
n(n-1)(n-2)!

3) cancel the (n-2)! on the bottom and top
4) foils out and factor as a quadratic

Question 11

Can “n” ever be a negative #

And why

Answer 11

Can’t have a negative amount of objects to pick from

Question 12

Permutations: how to answer grouped objects questions

Answer 12

1) ask yourself if you can rearrange the group and write that as a factorial (if you can’t continue as usual)
2) ask yourself if you can move the group and write that as just a # (if you can’t continue as usual)
3) how can you rearrange the rest of the positions and write that as a factorial
4) calculate

Question 13

What is a compliment

And when do we use it

Answer 13

Outcomes that don’t happen

Use it for “not” questions

Question 14

A group of 2 people don’t want to sit together, what would be the compliment

Answer 14

They do sit together

Question 15

What is the compliment formula

Not on sheet

Answer 15

Compliment=
(total with no restrictions)-(outcomes that do occur)

Both are written as factorials

Question 16

What is the formula for permutations with repeated objects

And what do the variables represent

Answer 16

n!/(a! b! c!)

Not on formula sheet

n= # of total objects
a b c= the same of one type (so don’t have to use all of them)

Question 17

How is VANCOUVER written in the perm formula for repeated objects

Answer 17

9!/ 2!

Question 18

What formula do square path questions use

Answer 18

Formula for permutations with repeated objects

Question 19

How to solve square path questions

Answer 19

1) count the number is increments vertical and count the number of increments horizontal
2) these two numbers are the bottom values in the reputation formula
3) add these two numbers to get the top value (n) in the report on formula
4) plug numbers in and calculate

Question 20

What is every value in the repetition formula written as

Answer 20

A factorial

Question 21

Why doesn’t the order matter in combinations

Answer 21

Because it creates the exact same group

Question 22

What are 3 examples of combinations

Answer 22

• committee where no roles are being served
• card hands
• lottery tickets

Question 23

What does “or mean”

Answer 23

Add

Question 24

What does “and” mean

Answer 24

Multiply

Question 25

How can you use “and” and “or” to help answer questions

Answer 25

Write out what is being asked in words using those words

Question 26

Cards: how many cards does each suit have

Answer 26

13

Question 27

How to solve combination problems involving “at least” or “at most” scenarios

Answer 27

1) find the # of outcomes for each individual scenario

2) add them up

Question 28

What is the first thing you must always do when solving a perm or comb question

Answer 28

Determine if it’s a perm or comb

Question 29

Can a question have a perm component and comb component

Answer 29

Yes

Question 30

Concept 4 example 3

Answer 30

Fill in

Question 31

Properties of binomial Theorem: there are _____ terms in the expansion

Answer 31

n+ 1

Question 32

Properties of binomial Theorem: the sum of the exponents x and y in EACH term is equal to _____

(And what does this look like)

Answer 32

_____

if n=5, x^3y^2

Question 33

Properties of binomial Theorem: the exponents of x ______ term by term from n to 0

Answer 33

Decrease

Question 34

Properties of binomial Theorem: the exponents of y ______ term by term from 0 to n

Answer 34

Increase

Question 35

Properties of binomial Theorem: the coefficients in each expansion form a symmetrical _____ array

Answer 35

Triangular

Question 36

In binomial thereom what does n have to be

Answer 36

A whole number

Question 37

How is pascals triangle limited

Answer 37

Have to write out every row before

Question 38

General term formula: what does k represent

Answer 38

One less than the term you want

Question 39

General term formula: what does n represent

Answer 39

The exponent of the binomial

Question 40

General term formula: what does x represent

Answer 40

First term of the binomial (no expansion)

Question 41

General term formula: what does y represent

Answer 41

Second term of binomial (not expansion)

Question 42

Binomial theorem: how do you solve question asking for the middle term

Answer 42

1) must be an odd number of terms on the expansion
2) n+1 = odd number
3) plug values into formula and solve

Question 43

Binomial theorem: how to solve when either x or y is unknown and so is k

Answer 43

1) find value of k by _____
4) solve for x or y by subbing values into general term formula and simplifying
5) make general term formula equal the term given and solve for x or y by isolating

Question 44

Binomial theorem: determine the numerical coefficient of the term containing a^7 in the expansion
(3-a)^10

Answer 44

1) plug values into general term formula
2) k=7
3) put everything into general term formula again and solve

Question 45

Binomial theorem: if asked for the constant term does this mean it’s the last term

Answer 45

No