I keep getting this wrong . Please tell me why

Question

A bag contains 6 red marbles, 6 white marbles, and 10 blue marbles. You draw 3 marbles out at random, without replacement. Give all answers as a decimal rounded to four places.

a) What is the probability that all the marbles are red?

The probability that all the marbles are red is 

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

The probability that exactly two of the marbles are red is    .

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

The probability of picking no red marbles is

Answer 1

6R, 6W, 10B sum to 22 marbles

draw 3 without replacement

a) P(3R) = 6/22 x 5/21 x 4/20 = 3/11 x 5/21 x 1/5 = 15/1155 = 1.2987% chance of 3 reds

c) P(R=0) 16/22 x 15/21 x 14/20 = 8/11 x 5/7 x 7/10 = 4/11 36.3636% = chance of no reds

b) P(2R 1N) = P(RRN) + P(RNR) + P(NRR)

= (6/22)(5/21)(16/20) + (6/22(16/21)(5/20) + (16/22)(6/21)(5/20)

= 3/11)(5/21)(4/5) + 3/11)(16/21)(1/4) + 8/11)(2/7)(1/4)

= 60/1155 + 48/924 + 16/308

=240/5(11)(7)(3)(4)(5) + 48)(3)/(5)/11)(7)3)4(5) + 16(5))6)/(11)(7)(3)(4)(5)

=

too many tedious calculations to avoid errors in less than 3 hours

= chance of exactly 2 reds in 3 draws without replacement

Answer 2

There are 22 total marbles, 6 are red, 16 are not

Hypergeometric Distribution applies here

a) C(6,3) * C(16,0)/C(22,3) = 20 * 16/1540 = 0.013

(where for example, C(6,3) is number of combinations of 3 out of 6)

want to pick 3 out of 6 red, none out of remaining marbles; will be picking 3 out of 22 total marbles

b) C(6,2) * C(16,1)/C(22,3) = 15 * 16/1540 = 0.1558

c) C(6,0) * C(16,3)/C(22,3) = 1 * 560/1540 = 0.3636