A bag contains 8 red marbles 7 white marbles and 8 blue marb

A bag contains 8 red marbles, 7 white marbles, and 8 blue marbles. You draw 5 marbles out at random, without replacement.

What is the probability that all the marbles are red?

Everything I have found on this type of question online says I\'m doing it right

(8/23)(7/22)(6/21)(5/20)(4/19) or (8 nCr 5)/(23 nCr 5) which is .0017 but the website keeps saying I am wrong. Is there something I\'m not seeing here?

What is the probability that exactly two of the marbles are red?

What is the probability that none of the marbles are red?

Solution

total number of possibilites = 23 C 5

a)

probability that all marbles are red = 8C5 / 23C5 = 0.00166

its the right way may some rounding error

so instead of rounding they just chopped the 6 , so try 0.0016

b)

required probability = 8C2 * 15C3 / 23C5 = 0.3786

c)

required probability = 15C5 / 23C5 = 0.08925