Question

You have a closed bag containing 10 marbles: 5 red, 3 green, 2 blue.

If you remove 3 marbles one-by-one, without replacement, what is the probability of getting 3 marbles in the order of green, red, blue?​

Answer 1

1/24

Explanation:

Each time you take one marble out, the total decreases by 1

You take 1 marble out, it decreases from 10 to 9 and there are now 9 marbles left in the bag.

When you will take the next marble, it will be on a total of 9 and after you take it out the total decreases again by 1. You'd have 8 and so on.

Green = 3

Red = 5

Blue = 2

Probability of getting it in the order RGB =

`(3)/(10) * (5)/(9) * (2)/(8) \: = (30)/(720) = (1)/(24)`