A bag contains some marbles, each of which is one of four colors (red, white, blue, and green). At least one of the marbles is red. The composition of the bag is such that if we take four marbles out at random (without replacement), each of the following is equally likely: (1) one marble of each color is chosen, (2) one white, one blue, and two reds are chosen, (3) one blue and three reds are chosen, (4) four reds are chosen. What is the smallest possible number of marbles in the bag?

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A bag contains some marbles, each of which is one of four colors (red, white, blue, and green). At least one of the marbles is red. The composition of the bag is such that if we take four marbles out at random (without replacement), each of the following is equally likely: (1) one marble of each color is chosen, (2) one white, one blue, and two reds are chosen, (3) one blue and three reds are chosen, (4) four reds are chosen. What is the smallest possible number of marbles in the bag?

Mathematics
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hm
let r,w,b,g equal the number of red,white,blue green marbles respectively let k = r+w+b+g, k is the total number of marbles (1) 1 marble of each color is chosen r/k * w/(k-1) * b/(k-2)* g/(k-3)= probability that each color is chosen (2) one white, one blue, and two reds are chosen, w/k * b/(k-1)*r/(k-2)*(r-1)/(k-3) you can do these (3) (4)
Wait I just get k=4r-6...

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Other answers:

see i help u
Sorry, but it didn't help me much because I still can't figure it out :(
hey flyingpie
@flyingpie you see k has to be an interger from here and u know r is atleast 1
So the smallest is 10?
can you take me to your question if u have other work up there i can see
@dan815 well at least 4 red because of problem statement, so 4(4)-6=10
Wait is k=4r-6 right @dan815
you cant really be sure, i need to see the rest of the work
you have to make sure that the solutions for white blue and green are also integers
4,3,2,1...
again lol.. i cant confirm your answer without work xD
i mean u can just plug those values in and see if it is working out
work: the probabilities have same denominator, but the numerators are rwbg=rwb(r-1)=r(r-1)(r-2)b=r(r-1)(r-2)(r-3), so g=r-1, w=r-2, b=r-3, and k=r+w+b+g=4r-6
It works but someone said that the answer is 21 from there packet...
ya there are infinite answers only 1 lowest
you can scale all the values up so that the probabilities still work out so
What do you think answer is @dan815
well im just going off by your statements, if u say u check it then 10 is the lowest i guess
(1) one marble of each color is chosen, (2) one white, one blue, and two reds are chosen, (3) one blue and three reds are chosen, (4) four reds are chosen. k=r+w+g+b rwgb = wbr*(r-1) = b*r*(r-1)*(r-2)=r*(r-1)(r-2)(r-3)
http://prntscr.com/88hp94 looks like it is right
but could you tell me what is smallest possible? is it 10? Thanks!
hello?

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