Question

An urn contains 7 white balls and 3 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 10 balls
a) If 2 balls are red?
b) If 3 balls are red and 2 are white?
c) If at leas 4 are red balls?

Answer 1

I'm trying to understand the problem.

Answer 2

I suppose I have to use combinations.

Answer 3

me too
are we taking out 3 or more?

Answer 4

it says 3 but then talks about if 4 are red...

Answer 5

three

Answer 6

so for the first are we assuming that 2 of the 3 we are taking out are red or...?

Answer 7

I guess. But if that is the case then I need to use a permutation.

Answer 8

that's what I'm confused on
if the first question is asking 'we draw 3 balls, how many ways can we do this of two of the three we take out are red?'
then I would say
3 ways to select red balls
7 ways to select the white ball
3*7=21
but then what about the rest?

Answer 9

that's if the balls are unique of course^

Answer 10

No they are not unique.

Answer 11

oh, well then I'm really confused.
I especially don't see how you can have 4 red balls when it says there are 3 in the urn..:/

Answer 12

Ahhh!

Answer 13

I made a mistake. I copy part of the problem below the one i wanted.

Answer 14

that makes sense

Answer 15

b) If all 3 balls are white.

Answer 16

c) If all 3 balls are red=

Answer 17

Sorry =/

Answer 18

well I still don't get the question. if it is as I said above and the balls are not unique, then...no I'm lost, sorry

Answer 19

Well at least I'm don't feel alone with the problem =)

Answer 20

I really want to understand this counting techniques.

Answer 21

lol
I'll be interested to see if someone understands it.
Buena suerte!

Answer 22

Thank you!

Answer 23

mindception

Answer 24

I think you were right TuringTest. They can be called: red_1, red_2, red_3, etc.

Answer 25

In that case I'm selecting 2 out of 7 white balls and 1 out of 3 red balls. So.

Answer 26

\[C(7,2)\cdot C(3,1)\]

Answer 27

I though the first was 2 red balls and one white

Answer 28

does the order that we pull them out in matter?
I guess it should, so my above answer is wrong.

Answer 29

Sorry my bad.

Answer 30

a) If2 balls are white and 1 is red.

Answer 31

The order matters, otherwise I'm lost.

Answer 32

yes, otherwise the answer to c) is 1

Answer 33

exactly!

Answer 34

Tu sabes español verdad T

Answer 35

TuringTest

Answer 36

well c) should still be the easiest:
3!=6

Answer 37

on poco
tengo que hacer la tarea para miercoles. no hice nada en lalas vacaciones!
estas de acuerdo conmigo acerca parte c) ?

Answer 38

un*

Answer 39

Ahh. What do you think about this: I help you with your spanish, and you can help me with my english.

Answer 40

What homework?

Answer 41

your english is a lot better than my spanish
I'm going to school here taking language classes
do you agree about part c?

Answer 42

I think the answer to c) is 1

Answer 43

only if the order doesn't matter

Answer 44

if it does then it is 6
do you want me to convince you?

Answer 45

Are you sure the order matters?

Answer 46

no

Answer 47

Me neither.

Answer 48

lol
oh man...

Answer 49

I'm going to draw some circles to represent the balls lol

Answer 50

me to I guess

Answer 51

Well Hero sometimes help with my english. Hi write something to him and he says: "No, you can write that in this way". I'm very grateful to him, but I'm ashamed that I can't not help him with something I know.

Answer 52

I was wondering if I can ask you similar things, and I can help you if you have spanish doubts.

Answer 53

Well even if you can't help me, you can always ask me if you have some doubts.

Answer 54

"can't not help him"
should be
"can't help him"

and I your the first mexican I've met who actually wants to help. All my friends just make fun of me.
anyhow
I see 6! ways te select 2 white balls out of 7

Answer 55

thanks by the way

Answer 56

I meant 6+5+4+3+2+1=21 ways to select the two white ones

Answer 57

But if the order matters It should be a permutation, so P(7,2) is not equal to 6! I think.

Answer 58

no, I was wrong about that sorry
my working theory is that the order does not matter and that there are 21 ways to select 2 white balls out of seven, and 3 ways to select the red one for each of those, so
21*3=63 ways for part a)
make any sense?

Answer 59

Yes! that makes sense!

Answer 60

ok then let's see if I have anything for b)...

Answer 61

I thought about selecting 3 whites out of 7, so C(7,3) = 35

Answer 62

I agree :D

Answer 63

well so then the answer is
a)63
b)35
c)1
IF the order of selection does not matter.
so what if it does???

Answer 64

Mmm good question, I'm thinking about it.

Answer 65

I don't think I know how to do those.

Answer 66

So you think this problem is done?

Answer 67

That would be great! hehe

Answer 68

I think you probably know better. Where did you get this problem? Does it seem like it should be so difficult as to have to consider order?
That seems extraneous to me, unless you have an advanced combinatorics book or something.

Answer 69

It is from the book: "College Algebra" written by Sullivan. It seems isa High School book.

Answer 70

Then I think we are done :)

Answer 71

Thank you =). And what do you have to do for homework?

Answer 72

I'm trying to figure out what my girlfriend just texted me...
chulos ojos de perrito enamorado
not sure what enamorado means, but it must be enamored, eh?
I have to do adverbs, practice past participle, negations, and... I don't know. A lot. I should have done it over break.

Answer 73

Are you in school?

Answer 74

enamorado means to be in love.

Answer 75

awww
well that's almost what enamored means

Answer 76

I finished my credits at college, I hope to get my undergraduated grade this year.

Answer 77

in what subject?

Answer 78

Mechatronics Engineering

Answer 79

I don't understand quite well what you mean with enamored. Does that word exist in english?

Answer 80

Dang, what math did you have to take for that?
I would think a lot, but it seems like you don't know too much more than me.

Answer 81

enamored means obsessed basically, but the word doesn't mean something quite as bad as obsessed

Answer 82

Ahh so you were almost right.

Answer 83

or 'awestruck'
like I'm enamored by the presence of somebody special
so almost...

Answer 84

well I took the basics matehmatics, Algebra, Linear Algebra, Analytic Geometry, Calculus, Probability(Even it seems I didn't), Differential Equations, Complex Analisys, etc.

Answer 85

Cool!
at UNAM ?

Answer 86

yes, How did you know?

Answer 87

because that's where I want to go

Answer 88

and you told me you lived in DF

Answer 89

Ohh, want do you want to study there?

Answer 90

What, sorry.

Answer 91

Whatever the highest physics I can get into is.

Answer 92

what sorry???

Answer 93

I mispelled something, nevermind. So you want a physic's PhD, at UNAM.

Answer 94

If I can. I don't know how they feel about gringos getting in though.
But UGDL sucks.

Answer 95

So you are studying at UGDL right now.

Answer 96

Why sucks?

Answer 97

Just two classes. Between that, moving here, and language I'm busy.
It's just a bad system in my opinion. They don't have high enough standards.

Answer 98

You mean academic standars, or administrative standars?