A box contains 10red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that i. all are blue? ii. at least one is green?

Explanation

Total number of marbles `=10+20+30=60`

Number of ways of drawing `5` marbles from 60 marbles `=(60)_(C_5)​`

(i) All the drawn marbles will be blue if we draw `5` marbles out of `20` blue marbles

`5` blue marbles can be drawn from 20 blue marbles in `(20)_(C_5)`​ ways

Probability that all marbles will be blue `=((20)_(C_5)​ )/((60)_(C_5))`