Question

EASY HELP: PLEASE: A bag contains two red marbles, three green ones, one lavender one, two yellows, and three orange marbles.

How many sets of four marbles include all the red ones?

Answer 1

i thought it was C(3,3)=1
C(9,1)=9 so i thought the answer was 9 but for some reason its wrong

Answer 2

oh hey @ganeshie8 :)

Answer 3

okay, so u wanto to choose 4 marbles

Answer 4

two marbles are are already choosen by god for u : 2 REDS are a must

Answer 5

sorry 2,2

Answer 6

that means you need to choose 2 more marbles

Answer 7

hmm so 2 more?

Answer 8

Count total number of marbles first

Answer 9

11 total

Answer 10

2R 3G 1L 2Y 3O

Answer 11

yes, 11 total.

and since 2 are in ur set already : you need to pick the remaining two from 11-2 = 9 marbles

Answer 12

how many ways u can choose 2 things from 9 ?

Answer 13

7

Answer 14

try again

Answer 15

oops

Answer 16

4.5?

Answer 17

3G 1L 2Y 3O :

2G,
1G, 1L
1G, 1Y
1G, 1O

1L, 1Y
1L, 1O

2Y,
1Y, 1O

2O

Answer 18

9 should be the correct answer right ?

Answer 19

did the grader marked it wrong ?

Answer 20

yes but for some reason it is wrong

Answer 21

might be a glitch in the system?

Answer 22

yes

Answer 23

let me think a bit more..

Answer 24

ok

Answer 25

9 should be correct

Answer 26

@iambatman wat do u think

Answer 27

yeah exactly hmm

Answer 28

if we consider each marble is identifiable as diffierent, then :

http://www.wolframalpha.com/input/?i=%283+choose+2%29%2B%283+choose+1%29%281+choose+1%29%2B%283+choose+1%29*%282+choose+1%29%2B%283+choose+1%29*%283+choose+1%29%2B+%281+choose+1%29*%282+choose+1%29%2B%281+choose+1%29*%283+choose+1%29%2B+%282+choose+2%29%2B%282+choose+1%29*%283+choose+1%29%2B+%283+choose+2%29

Answer 29

maybe try entering 36 once

Answer 30

yeah it was 36 hmm but why not 9?

Answer 31

cool :) they want u treat each marble as different :

think of the 3 green marbles as : {G1, G2, G3}

Answer 32

dont think of them as : {G, G, G}

Answer 33

oh so you multiply them all?

Answer 34

3G 1L 2Y 3O :

then total number of sets having 2R and 2G marbles would be :
\(\large^3C_2 \)

Answer 35

cuz, u can choose 2 Green marbles from 3 Green marbles in : \(\large^3C_2\) ways

Answer 36

and C is the total added together correct

Answer 37

yes you need to add up all cases

Answer 38

check the wolfram link :)

Answer 39

ok awesome thank you! :) @ganeshie8

Answer 40

2 Green : \(\large ^3C_2\)
1 Green 1 Lavender : \(\large ^3C_1 \times ^1C_1\)
1 Green 1 Lavender : \(\large ^3C_1 \times ^2C_1\)
1 Green 1 Orange : \(\large ^3C_1 \times ^3C_1\)
.......

Answer 41

add up all the cases... wolfram link shows the exact same

Answer 42

ok awesome! @ganeshie8

Answer 43

np :) @mathfriend any other shortcut u have other than the dumb method i suggested ?

Answer 44

i think there might be a shortcut @ganeshie8 i can't think of it at the moment lol

Answer 45

Basically, there are 2 red marbles, and 9 other marbles. So you're looking at how many combinations can these 9 marbles make by taking 2 at a time. 9*8/2 = 36...Does this make sense?

Answer 46

The wording to this question is terrible, that's why it's tricky :p

Answer 47

that makes perfect sense now after looking at it again xD

Answer 48

it does!

Answer 49

i hate the wording at times haha

Answer 50

Haha, sorry for the late reply, I kept thinking I was wrong...so I had to keep rereading the damn question.

Answer 51

no worries its ok its cool to learn both ways !!

Answer 52

Alright, time for me to go fight crime, g'night :p

Answer 53

thanks @iambatman , u deserve a good night's sleep ! embrace urself tightly and sleep :) good night !!

Answer 54

haha awesome good night!!!

Answer 55

Thank you @ganeshie8 good night, and take care! @hogwardsacademy Good night, and good luck!

Answer 56

Thank you! @iambatman

Answer 57

Hmmmm..... I would have said a required set would look something like {R,R,G,L} or {O,Y,R,R} or {R,O,O,R} etc. and its how many of these you can have. Lets look at the sets whereby the two reds come at the start and lavendar - if present at all - comes at the end. Then you have the following distinct 9 sets:

{ R, R, G, G } { R, R, Y, Y } { R, R, O, O }

{ R, R, G, Y } { R, R, G, O } { R, R, G, L }

{ R, R, Y, O } { R, R, Y, L }

{ R, R, O, L }

So if the order was not important, the answer would be 9. If the order was relevant then then each of the first 3 sets can be arranged 6 unique ways. Each of the remaining 6 can be re-organised into 12 distinct sets - giving 3 x 6 + 6 x 12 = 90

So I would have said 90. But I guess it comes down to the interpretation of the question.

Answer 58

I see, yeah the problem must be formulated a bit more clearly...