## No-data 3 years ago 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?

1. No-data

I'm trying to understand the problem.

2. No-data

I suppose I have to use combinations.

3. TuringTest

me too are we taking out 3 or more?

4. TuringTest

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

5. No-data

three

6. TuringTest

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

7. No-data

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

8. TuringTest

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?

9. TuringTest

that's if the balls are unique of course^

10. No-data

No they are not unique.

11. TuringTest

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..:/

12. No-data

Ahhh!

13. No-data

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

14. TuringTest

that makes sense

15. No-data

b) If all 3 balls are white.

16. No-data

c) If all 3 balls are red=

17. No-data

Sorry =/

18. TuringTest

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

19. No-data

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

20. No-data

I really want to understand this counting techniques.

21. TuringTest

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

22. No-data

Thank you!

23. notsmart

mindception

24. No-data

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

25. No-data

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

26. No-data

$C(7,2)\cdot C(3,1)$

27. TuringTest

I though the first was 2 red balls and one white

28. TuringTest

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

29. No-data

30. No-data

a) If2 balls are white and 1 is red.

31. No-data

The order matters, otherwise I'm lost.

32. TuringTest

yes, otherwise the answer to c) is 1

33. No-data

exactly!

34. No-data

35. No-data

TuringTest

36. TuringTest

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

37. TuringTest

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

38. TuringTest

un*

39. No-data

40. No-data

What homework?

41. TuringTest

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

42. No-data

I think the answer to c) is 1

43. TuringTest

only if the order doesn't matter

44. TuringTest

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

45. No-data

Are you sure the order matters?

46. TuringTest

no

47. No-data

Me neither.

48. TuringTest

lol oh man...

49. No-data

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

50. TuringTest

me to I guess

51. No-data

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.

52. No-data

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

53. No-data

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

54. TuringTest

"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

55. TuringTest

thanks by the way

56. TuringTest

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

57. No-data

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

58. TuringTest

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?

59. No-data

Yes! that makes sense!

60. TuringTest

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

61. No-data

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

62. TuringTest

I agree :D

63. TuringTest

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???

64. No-data

Mmm good question, I'm thinking about it.

65. TuringTest

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

66. No-data

So you think this problem is done?

67. No-data

That would be great! hehe

68. TuringTest

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.

69. No-data

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

70. TuringTest

Then I think we are done :)

71. No-data

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

72. TuringTest

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.

73. TuringTest

Are you in school?

74. No-data

enamorado means to be in love.

75. TuringTest

awww well that's almost what enamored means

76. No-data

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

77. TuringTest

in what subject?

78. No-data

Mechatronics Engineering

79. No-data

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

80. TuringTest

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.

81. TuringTest

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

82. No-data

Ahh so you were almost right.

83. TuringTest

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

84. No-data

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

85. TuringTest

Cool! at UNAM ?

86. No-data

yes, How did you know?

87. TuringTest

because that's where I want to go

88. TuringTest

and you told me you lived in DF

89. No-data

Ohh, want do you want to study there?

90. No-data

What, sorry.

91. TuringTest

Whatever the highest physics I can get into is.

92. TuringTest

what sorry???

93. No-data

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

94. TuringTest

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

95. No-data

So you are studying at UGDL right now.

96. No-data

Why sucks?

97. TuringTest

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.

98. No-data

99. TuringTest

academic was what I meant, but I'm sure administrative as well. My girlfriend had 4/6 of her graphic design teachers be about 25 years old. I'm almost that old! Not exactly tenure...

100. No-data

Well the teachers here are very old hehe.

101. No-data

but there is a good academic level too.

102. No-data

But I think that the best option is at Cinvestav, have you heard of it?

103. TuringTest

no, where's that?

104. No-data

It's has several (places?) on the country, Queretaro, D.F, I'm not sure if Guadalajara.

105. TuringTest

I'll look into it. wrote the name down

106. No-data

There you can find the best academic level in the country.It is difficult to get in.

107. No-data

CINVESTAV

108. TuringTest

brief english lesson: It's has several (places?) on the country It has several locations in the country ^^^correct

109. No-data

Ohh thank you, that is what i meant with my bad english!

110. No-data

111. TuringTest

I wish you could just give me little tips like that in spanish, but I've only been taking classes for 2 1/2 months. It'll be awhile befor I'm fluent :( -there is?!?!?

112. No-data

Don't worry feel free to write in spanish. That is the best way to learn, by practicing

113. No-data

(there is is wrong?)

114. TuringTest

Thanks for not laughing at me... or at least thanks for not writing lol!! what 'there is'? where

115. TuringTest

oh mine that was to your last comment about there being a school here I went 'there is?" out of surprise

116. No-data

Don't worry =P. I was telling you that there is a Cinvestav located on Guadalajara.

117. No-data

ahh ok hehe

118. No-data

You can take a look here: http://www.cinvestav.mx/posgrado.aspx

119. No-data

Does you gf speaks english?

120. No-data

I even have some of the (admission or entrance?) exams. Let me see..

121. TuringTest

Yeah, which has really slowed me down. She has no patience. Everytime I ask her something she says 'that's stupid, why would you ask that?' I will be looking into that school here, I kinda like Guadalajara, and after living in LA for 12 years I don't really want to move to DF more expensive to, right?

122. TuringTest

cool! entrance exam is the term, what is it in spanish?

123. No-data

Examen de admisión. That is the reason I get confused.

124. TuringTest

right, I tried to say pagar atencion once, I got laughed at, but that's what it is in english "pay attention" not "put attention"

125. TuringTest

again sorry for not having accent marks...

126. No-data

Don't worry 70% of mexicans don't know how to use the accent marks.

127. No-data

But is good that you learn how to use them.

128. TuringTest

My roomate spoke spanish at home all his life and was born in DF, but I correct him on things sometimes because I'm learning spanish formally. He never did that.

129. No-data

You mean your roomate at LA?

130. TuringTest

No, here in GDL

131. No-data

Ahh.

132. TuringTest

I think we have the same time zone, right? I know it's not that late, but I think I should try to sleep. I have to do 2 weeks worth of homework tomorrow =(

133. No-data

Yeah, it's better to go to sleep. I'm still looking for the entrance exam.

134. TuringTest

Thanks for the info on Cinvestav, I'll look into it. And looking for the exam. If you find it I'd be curious to hear what it has.

135. No-data

Ok, Have a good night, I'm goint to be here tomorrow in case you need some help.

136. TuringTest

I may have to take you up on that, thanks! goodnight No-Data.

137. No-data

to what?

138. No-data

what does it means to take something up?

139. TuringTest

"to take someone up on an offer" I said I'd have to take you up on your offer, meaning I may ask you for help with spanish.

140. TuringTest

or just, 'I might take you up on that' for short

141. No-data

Ahh thanks!

142. No-data

Well is difficult to learn that in a book or with google traslator. thank you so much. And have a good night again

143. TuringTest

yeah expressions are tricky... goodnight :D