SOLUTION: A box contains 20 balls out which 7 are white balls, 5 are black balls, 6 are
red balls and 2 are yellow balls. If four balls are drawn at random. What is
the probability that ba
Algebra ->
Probability-and-statistics
-> SOLUTION: A box contains 20 balls out which 7 are white balls, 5 are black balls, 6 are
red balls and 2 are yellow balls. If four balls are drawn at random. What is
the probability that ba
Log On
Question 1184465: A box contains 20 balls out which 7 are white balls, 5 are black balls, 6 are
red balls and 2 are yellow balls. If four balls are drawn at random. What is
the probability that balls of one colour, balls of two colours and balls of three colours are drawn? Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! there are 20C4 ways to draw 4 balls=4845
one color
white is 7C4/20C4=35/4845 and may be reduced.
black is 5C4/20C4=5/4845
red is 6C4/20C4=15/4845
yellow is 0 since there must be at least 4 of them.
balls of 1 color has probability of 55/4845 of being drawn
--
two colors would be
(same denominator or 4845)
white black
7C1*5C3+7C2*5C2+7C3*5C1=70+210=175=455
-
white red
7C1*6C3+7C2+6C2+7C3*6C1=140+315+210=665
-
white-yellow
7C2*2C2+7C3+2C1=21+70=91
-
black-red
5C1*6C3+5C2*6C2+5C3*6C1=100+150+60=310
-
black-yellow
5C2*2C2+5C3*2C1=30
-
red-yellow
6C2*2C2+6C3*2C1=55
Total for these is 1606/4845
-----
w-b-r
7C2*5C1*6C1+7C1*5C2*6C1+7C1*5C1*6C2=630+420+525=1575
w-b-y
7C2*5C1*2C1+7C1*5C2*2C1+7C1*5C1*2C2=210+140+35=385
-
w-r-y
7C2*6C1*2C1+7C1*6C2*2C1+7C1*6C1*2C2=252+210+42=504
-
b-r-y
5C2*6C1*2C1+5C1*6C2*2C1+5C1*6C1*2C2=120+150+30=300
That total is 2764/4845
-
Not asked for but balls of 4 colors would be 7C2*5C1*6C1*2C1=420/4845
55+1606+2764+420=4845, and that accounts for all the possibilities.
