Question

combinations unordered subsets h e l p

Answer 1

this video might help
https://www.khanacademy.org/math/trigonometry/prob_comb/combinatorics_precalc/v/permutations

Answer 2

You have 5 items to choose for the first slot

After picking the first item, and assuming you cannot pick it again, you have 4 items to choose from for the second slot

Answer 3

So if order mattered, then you would have 5*4 = 20 different ways to pick the 5 entrees

Answer 4

But order doesn't matter, so how do we fix this?

Answer 5

I have no idea, lol a little more help?

Answer 6

say that you have the five entrees labeled A, B, C, D, E

Answer 7

if you pick entrees A and D

that's the same as picking entrees D and A

agreed?

Answer 8

Use:
http://www.mathsisfun.com/combinatorics/combinations-permutations.html

https://www.khanacademy.org/math/trigonometry/prob_comb/combinatorics_precalc/v/permutations

This might help. Also use your textbook.

Answer 9

I don't have a textbook lol it's online school @some_someone and @jim_thompson5910 I already skipped the question, and now I'm on another one -

Answer 10

well we were nearly done, just gotta be patient lol

Answer 11

we have 20 different ways to pick 2 entrees if order mattered

but order doesn't matter, so you have to divide by 2 to correct for the double counting

Answer 12

well if you dont have a textbook, surely you must have been given notes by your instructor. @CassieStyles8x

Answer 13

@jim_thompson5910 oops I can't go back to the previous question, so can you help me with the one I just posted?

Answer 14

ok we have 10 members

and they shake hands with the rest of the members

Answer 15

this means we have 10 choices for slot 1 and 10-1 = 9 choices for slot 2

so we have 10*9 = 90 different hand shakes....if order mattered

Answer 16

but Bill shaking hands with Ted is the same as Ted shaking hands with Bill because order doesn't matter

so 90 is an overcount (we're counting each handshake twice)

Answer 17

so how do you fix that?

Answer 18

90 is too much right?

Answer 19

yes

Answer 20

the actual count is much smaller

Answer 21

so without it being 90 the handshakes are only being counted as one handshake or two?

Answer 22

if you got 90, then you are counting each handshake twice

to correct this, you divide by 2 to get 90/2 = 45

this means that there are 45 distinct handshakes (ie distinct people shaking hands)

Answer 23

okay thankyou so much , do you have time to help me with a few more?

Answer 24

sure just a few though

Answer 25

Okay.. How many ways can you choose steak, fish, or chicken if you can only choose 2 meats?

Answer 26

how many choices for the first slot

Answer 27

2?

Answer 28

you sure?

Answer 29

steak
fish
chicken

I count 3

Answer 30

oh yeah woops I meant to push 3

Answer 31

so you have 3 choices for the first slot

then you have 2 choices for the second slot

Answer 32

giving you 3*2 = 6 choices total

IF order mattered

Answer 33

but you're overcounting again because order doesn't matter

Answer 34

how much is the difference?

Answer 35

well picking chicken and fish for example is the same as picking fish and chicken

Answer 36

so we're counting each pair twice

Answer 37

3 ways?

Answer 38

good 6/2 = 3

Answer 39

so your three possible ways are


steak, chicken
steak, fish
chicken, fish

Answer 40

Got it thanks... A certain pizza parlor has seven different toppings. How many two-topping pizzas are possible?

Answer 41

how many choices for the first slot

Answer 42

7?

Answer 43

you pick one of those 7 choices and you put it in the first slot

how many choices do you have left for slot 2?

Answer 44

5? or 6?

Answer 45

why 5

Answer 46

you start with 7 choices

you pick ONE choice and you put it into slot 1

you will be left with 7-1 = 6 choices

Answer 47

so you have 7 choices for slot 1

you have 6 choices for slot 2

Answer 48

7*6 is 42

Answer 49

that's how many ways to do it if order mattered

but it doesn't

Answer 50

so you have to divide by 2 to correct this double-counting

Answer 51

divide 42 by 2?

Answer 52

yes

Answer 53

the answer is 21

Answer 54

good

Answer 55

How many ways can a committee of 4 people be chosen from a group of 8 people?

Answer 56

you have 8 choices for slot 1

you have 7 choices for slot 2

you have 6 choices for slot 3

you have 5 choices for slot 4


See the pattern?

Answer 57

yes I do

Answer 58

ok multiply 8, 7, 6, 5

the result would be the answer if order mattered

but again....order doesn't matter

so you have to divide by 4*3*2*1 = 24 to correct this overcounting

Answer 59

answer is 70?

Answer 60

perfect

Answer 61

so hopefully you see how we're getting all this?

Answer 62

Yes. A pizza restaurant has hamburger, pepperoni, canadian bacon, and sausage. How many ways can a three-topping meat pizza be made?

Answer 63

ok tell me what you get using this process we've been doing

Answer 64

there's 4 ways you can do it, slot 1 is 4?

Answer 65

good, slot 2 is ???

Answer 66

3?

Answer 67

slot 3 is ???

Answer 68

@jim_thompson5910 i hope @CassieStyles8x is getting the concept cause your a really great teacher. And if she is not understanding and just want the answers she is hurting herself since she is not learning. @jim_thompson5910 AMAZING JOB +100

Answer 69

@some_someone I'm definitely getting all of it now thank you @jim_thompson5910

Answer 70

thanks some_someone, but I think CassieStyles8x is getting the concept

it's definitely a strange concept at first until you practice with it a bit

Answer 71

yw CassieStyles8x

Answer 72

slot 3 is ???

Answer 73

slot three is 2

Answer 74

multiply the numbers in each slot

Answer 75

4*3*2 = ??

Answer 76

24

Answer 77

now you have to correct for the overcount

Answer 78

so you divide by 3*2*1 = 6

Answer 79

4 yay

Answer 80

Basically if you have 10 slots, then you would start with 10, move to 9, move to 8, etc all the way down to 1

So if you had 10 slots, then you would divide by 10*9*8 ...*3*2*1 = 3,628,800

to correct for overcounting

Answer 81

good, it is 4

Answer 82

During a lunch seminar chocolate, caramel and strawberry toppings were available. How many two-topping sundaes are possible?

Answer 83

slot 1 has how many choices

Answer 84

3 choices

Answer 85

slot 2 has ____ choices

Answer 86

2 and slot 1 has 1 so 3*2*1=6

Answer 87

there are only 2 slots this time

Answer 88

so 3*2=6

Answer 89

but luckily, that extra 1 at the end makes no difference

Answer 90

better

Answer 91

6 is the count if order mattered, but it doesn't

there are 2 slots, so you have to divide by 2! = 2*1 = 2 to correct for overcounting

so 6/2 = 3

which means there are 3 ways to do this since order doesn't matter

Answer 92

those 3 ways are

chocolate, caramel
chocolate, strawberry
caramel,strawberry

Answer 93

thank you you just saved my life and helped me understand it because the videos my teacher gave me doesn't help me at all

Answer 94

glad to be of help, and I'm sry to hear that