Question

Suppose 80 points are placed around a circle. A line segment is drawn between each pair of points.How many line segments are drawn?

Answer 1

you have 80 points along a circle and you have to choose 2 of them to make a line segment
the number of ways to do this is \(\binom{80}{2}\) some times written as \(_{80}C_2\) and read "80 choose 2"

Answer 2

you know how to compute that number?

Answer 3

I have not idea

Answer 4

i take it this is some combinatorics class
or maybe probability?

Answer 5

it is my MGF1107 class LIberal Art II

Answer 6

liberal arts?! lol have fun
actually it is the same idea as your previous problem

Answer 7

\[\binom{80}{2}=\frac{80\times 79}{2}\]

Answer 8

yeah I am completely lost

Answer 9

would the answer be 3160

Answer 10

yeah i can see
what you need to know is a formula for \(\binom{n}{k}\) the number of ways you can choose \(k\) items from a set of \(n\)

Answer 11

ok

Answer 12

the formula is
\[\binom{n}{k}=\frac{n!}{k!(n-k)!}\] but you don't really use it exactly in this form
have you seen this before?

Answer 13

no

Answer 14

oh
then i don't know how you are expected to do the problem without it
what methods are you supposed to use?

Answer 15

you certainly don't have time to count them all!

Answer 16

I am not sure because this math class is online

Answer 17

you got a book?

Answer 18

yeah online and I am lost in the book

Answer 19

I dont see the formula in the book at all

Answer 20

hmm you need it for the last problem you asked as well, the maze problem

Answer 21

maybe it is written as \(_nC_k\)

Answer 22

is there anything there about pascal's triangle?

Answer 23

I know i posted the maze i dont know if you can click on the link i posted

Answer 24

http://www.coursesmart.com/9781285221540/firstsection?portal=coursesmart&CSTenantKey=cengage&key=A9438807DBF48783826B50DD6D3AF8BF0E7FAF703C07BD9FEE00354F9C01481B6CEBCCEC35541EDEFC045B8A42CB4BF49E2E2807289730B0BEF8983EAAC74E2A5B5626976C2002694A3760266CA6BC3D23E6EF808A5754D6FD40FE6B57F0B7B9E9195060C5FDA2C9D4F8D10885DA3B79870BE547A0CCEC8CD35BC6D533CF35E6&spid=&TenantOption=cengagebrain#X2ludGVybmFsX0J2ZGVwRmxhc2hSZWFkZXI/eG1saWQ9OTc4MTI4NTIyMTU0MC8yNA==

Answer 25

let me see if i can find it, i can help you with that one as well

Answer 26

thank you I sent you the link to my book

Answer 27

yeah i got it
what page are you on?

Answer 28

problem solving

Answer 29

do you know what page it is?

Answer 30

page 13

Answer 31

page 14

Answer 32

jeez you are right, i guess you are just supposed to "figure it out"

Answer 33

let me find your last problem and see if i can help you with it

Answer 34

ok thank you

Answer 35

I am so lost thank you for helping

Answer 36

could you repost? i can't find the damned problem

Answer 37

yeah

Answer 38

you can put it here if you like

Answer 39

Morris Mouse can easily find his way through the maze from the entrance A to the exit B. However, he only receives food if he finds the exit without going west or south. (North is towards the top of the page.) How many different paths can he take through the maze to receive food? (Note: Different paths have at least one distinct section. See the diagram for an example.)

https://angel.spcollege.edu/AngelUploads/QuestionData/2bfb73e4-236a-4599-bf10-af270b97f4c8/61324442322642544448.png# {7a7875da-913f-49bb-a105-e7c68ffc0aca}

Answer 40

ok

Answer 41

ok now before we do this one lets redo the first one with a method that might be more suitable

Answer 42

ok

Answer 43

pick one of the 80 points
it has 79 places to go
pick the next one
it has 78 place to go (because you don't want to count the first one twice)
pick the next one
it has 77 places to go
etc

Answer 44

so you can solve this by adding
\[79+78+77+76+...+2+1\] or
\[1+2+3+...+77+78+79\] now i do notice that you have a formula for this in the book

Answer 45

ok

Answer 46

the formula is
\[1+2+3+...+n=\frac{n(n+1)}{2}\] which in your case is
\[\frac{79\times 80}{2}\] same exact answer as before

Answer 47

3160 was the answer

Answer 48

yes

Answer 49

now for the next one, i cannot think of simple explanation but i can explain it

Answer 50

i have 10 questions to do. Can you help me with them

Answer 51

Thank you. Your such a big help

Answer 52

lol sure until i get tired

Answer 53

lol ok thank you. I need to pass this class for my RN degree

Answer 54

in the maze problem you have, you can think of it this way:
you have to go to the right 5 times and up 5 times, in some order

Answer 55

ok I am looking at it now

Answer 56

let me know when it is clear that you are going to take 5 steps right and 5 steps up to get from point A to point B

Answer 57

ok so I took 5 steps to the right and 5 up

Answer 58

that would give me 25 steps

Answer 59

now the question is, how many ways can you do that
here is one way
\[(r, r, u, r, u, u, r, u, r, u)\]

Answer 60

ok

Answer 61

if i replace all \(r\) by \(0\) and all \(u\) by \(1\) we turn
\[(r, r, u, r, u, u, r, u, r, u)\] in to
\[(0,0,1,0,1,1,0,1,0,1)\]

Answer 62

now I am lost

Answer 63

forget that then, it is unnecessary

Answer 64

sorry

Answer 65

the question is, how many ways can i fill ten slots with 5 \(r\) and 5 \(u\)

Answer 66

oh ok

Answer 67

now we have to use the formula i wrote above
i see no way around it

Answer 68

ok let me right that formula down

Answer 69

the question translates in to this
"how many ways can i pick 5 out of the 10 slots to put an \(r\)?"

Answer 70

and the answer is
\[\binom{10}{5}=\frac{10\times 9\times 8\times 7\times 6}{5\times 4\times 3\times 2}\]

Answer 71

as i said this i called "10 choose 5" and we can ask wolfram for the answer, although this is very easy to compute if you cancel first and multiply last

Answer 72

ok let me solve this

Answer 73

ok

Answer 74

252 is the answer

Answer 75

yes

Answer 76

thank you!!

Answer 77

yw
next?

Answer 78

What is the 76th decimal digit in the decimal representation of

Answer 79

13/11

Answer 80

that can't be that hard, you only have two to choose from

Answer 81

What is the 76th decimal digit in the decimal representation of 13/11

https://angel.spcollege.edu/AngelUploads/QuestionData/acae6292-47fd-4c42-9c1a-f19417bc9091/62K31R313554314L4653.png# {2752460f-f064-4665-9c63-2331704bfd48}

Answer 82

76 is an even number right?

Answer 83

so it is 8

Answer 84

lots easier than the last two by far

Answer 85

yes that is what i got

Answer 86

lol

Answer 87

ok
i hope the rest are that easy

Answer 88

If two ladders are placed end to end, their combined height is 46.5 feet.One ladder is 3.5 feet shorter than the other ladder.What are the heights of the two ladders?

Answer 89

we are on number 5

Answer 90

you got lots of way to do this
you can write an equation if you like
or just guess and check

Answer 91

ok what way would be the easy

Answer 92

i am always accused of doing this the not math way but if it was me i would guess
if one is 20 and the other is 3.5 longer then it would be 23.5
but then the total would only be \(20+23.5=43.5\) so that is not the right answer
try a bigger one

Answer 93

ok

Answer 94

if you want an equation, call one length \(x\) so the other would be \(x+3.5\) and then solve
\[x+x+3.5=46.5\]

Answer 95

or as we say in math,
\[2x+3.5=46.5\]

Answer 96

can you solve that one? takes two steps
subtract \(3.5\) from both sides, divide both sides by \(2\)

Answer 97

ok 21.5

Answer 98

answer would be 21.5 feet and 18 feet