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

Sol: 1. This has at least 2 yellow meaning..

a> there can be all three Y => 4c3
OR
b> 2 Y and 1 out of 2 R and 3 B => 4c2 x 5c1

Total 34

2.This has exactly 1 Y and remaining 2 out of 5 = > 4c1 x 5c2

Total 40
Total possibilities = (9!/3!6!) = 84
Adding the two probabilities: probability = 74/84 = 37/42


I solved it like
prob of it being Jaune X = 4/9 x 3/8 x 2/7 + 4/9 x 3/8 x 5/7 = 1/3
prob of it being Jaune Y = 4/9 x 5/8 x 4/7 = 10/63

Total prob of being jaune = 1/3 + 10/63 = 31/63.
Whats wrong with this method? :