A bag contains some marbles, each of which is one of four colors (red, white, blue, and green). There is at least one of each color. 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?
As mentioned in the question, each of the following provided options is equally likely, the bag should contain
atleast 4 red marbles to satisfy option 4
atleast 1 blue marble in addition to above to satisfy option 3
atleast 1 white marble in addition to above to satisfy option 2
Also the question states that there are atleast one of each color - so we need to account for green marble
atleast 1 green marble in addition to above to statisfy option 1
so adding it all together 4R + 1B + 1W + 1G = 7 marbles
See a couple of solutions here: https://web2.0calc.com/questions/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-comp
And here: https://artofproblemsolving.com/wiki/index.php?title=1996_AHSME_Problems/Problem_26