Kurt, a painter, has 9 jars of paint:
4 are yellow
2 are red
rest are brown
Kurt will combine 3 jars of paint into a new container to make a new color, which he will name accordingly to the following conditions:
Brun Y if the paint contains 2 jars of brown paint and no yellow
Brun X if the paint contains 3 jars of brown paint
Jaune X if the paint contains at least 2 jars of yellow
Jaune Y if the paint contains exactly 1 jar of yellow
What is the probability that the new color will be Jaune
a) 5/42
b) 37/42
c) 1/21
d) 4/9
e) 5/9
Source: https://www.beatthegmat.com/difficult-gm ... 8.html#116
I started solving this problem and was struck with a fundamental doubt. If there are n identical objects and if we are to make groups of r objects (r < n), how many groups (or combinations) are possible?
If the objects are not identical, then it is nCr = n! / ((n - r)! x r!). But what if the objects are identical, is it the same?
Take for example, the 4 yellow jars in the question.
Case 1: If they are non-identical i.e. Y1, Y2, Y3, Y4 then the number of ways of picking 3 jars is 4C3.
Case 2 (this is what I'm confused about): If the yellow jars are all identical, Y, Y, Y and Y. Any 3 that I pick are going to be the same YYY and I won't be able to differentiate which 3 these are. So is the number ways of picking 3 jars out of the 4 identical ones in the case 1?
I would really appreciate help from any of the experts.
4 are yellow
2 are red
rest are brown
Kurt will combine 3 jars of paint into a new container to make a new color, which he will name accordingly to the following conditions:
Brun Y if the paint contains 2 jars of brown paint and no yellow
Brun X if the paint contains 3 jars of brown paint
Jaune X if the paint contains at least 2 jars of yellow
Jaune Y if the paint contains exactly 1 jar of yellow
What is the probability that the new color will be Jaune
a) 5/42
b) 37/42
c) 1/21
d) 4/9
e) 5/9
Source: https://www.beatthegmat.com/difficult-gm ... 8.html#116
I started solving this problem and was struck with a fundamental doubt. If there are n identical objects and if we are to make groups of r objects (r < n), how many groups (or combinations) are possible?
If the objects are not identical, then it is nCr = n! / ((n - r)! x r!). But what if the objects are identical, is it the same?
Take for example, the 4 yellow jars in the question.
Case 1: If they are non-identical i.e. Y1, Y2, Y3, Y4 then the number of ways of picking 3 jars is 4C3.
Case 2 (this is what I'm confused about): If the yellow jars are all identical, Y, Y, Y and Y. Any 3 that I pick are going to be the same YYY and I won't be able to differentiate which 3 these are. So is the number ways of picking 3 jars out of the 4 identical ones in the case 1?
I would really appreciate help from any of the experts.
-- Santhosh S
