help with a question

Question

A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement). (a) What is the probability that one will be green and the other red? (b) What is the probability that one will be blue and the other yellow?

 

So out of what is stated this is what I have come up with so far.. other than that i am lost.

BLUE 10/20 (50%)

RED 5/20 (25%

GREEN 4/20 (20%)

YELLOW 1/20 (5%)

Answer 1

P(one green, one red) = (# of ways to choose a green)(# ways to choose a red) ÷ (# ways to choose 2 marbles from 20).

 

Using Binomial Coefficient Notation nCr = (n! / [r! (n-r)! ], the above denominator is 20C2 = 190.

The above numerator is simply 4•5 so the answer is 20/190 = 2/19