A box contains 5 red balls, 4 orange balls, and 3 yellow balls; and each ball has the same size. If you randomly remove six balls from the box without replacement, what is the probability of removing the balls in this sequence: red,yellow,red,yellow,orange,yellow? In how many ways can you remove (without replacement) 3 balls of each color from the above mentioned box? Solution Initially, Number of Red balls = 5 Number of Orange balls= 4 Number of Yellow balls = 3 Therefore, Total number of balls in the box = 5 + 4 + 3 = 12 Probability that the first ball removed is Red = (5/12) Probability that the first ball removed is Red and second ball removed is Yellow = (5/12)*(3/11) Similarly, Probability of removing the balls in the sequence: red,yellow,red,yellow,orange,yellow = (5/12)*(3/11)*(4/10)*(2/9)*(4/8)*(1/7) = 0.000722 3 balls of Red color can be removed in 5C3 ways. 3 balls of Orange color can be removed in 4C3 ways. 3 balls of Yellow color can be removed in 3C3 ways. So, 3 balls of each color can be removed from the box in (5C3)*(4C3)*(3C3) = 40 ways..

1. A box contains 5 red balls, 4 orange balls, and 3 yellow balls; and each ball has the same size.
If you randomly remove six balls from the box without replacement, what is the probability of
removing the balls in this sequence: red,yellow,red,yellow,orange,yellow?
In how many ways can you remove (without replacement) 3 balls of each color from the above
mentioned box?
Solution
Initially,
Number of Red balls = 5
Number of Orange balls= 4
Number of Yellow balls = 3
Therefore, Total number of balls in the box = 5 + 4 + 3 = 12
Probability that the first ball removed is Red = (5/12)
Probability that the first ball removed is Red and second ball removed is Yellow = (5/12)*(3/11)
Similarly, Probability of removing the balls in the sequence:
red,yellow,red,yellow,orange,yellow
= (5/12)*(3/11)*(4/10)*(2/9)*(4/8)*(1/7)
= 0.000722
3 balls of Red color can be removed in 5C3 ways.
3 balls of Orange color can be removed in 4C3 ways.
3 balls of Yellow color can be removed in 3C3 ways.
So, 3 balls of each color can be removed from the box in (5C3)*(4C3)*(3C3) = 40 ways.