Suzan sees a bag of marbles, she grabs a handful at random. she has seen a bag containing four red marbles, three green ones, four white ones, and three purple ones. she grabs five of them. find the probability of the following event, expressing it as a fraction in lowest terms. she has two green ones and one of each of the other colors.

In this question, Suzan is taking 5 marble from a bag containing 4 red marbles, 3 green ones, 4 white ones, and 3 purple ones. The total marble in the bag should be: 4+3+4+3= 14. The question is how much the probability to get 1 red, 2 green, 1 white and 1 purple.

Ways to take 5 marble out of 14=14C5= 14!/5!9!= 2002
 
Ways to take 1 red marble out of 4= 4C1= 4

Ways to take 2 green marble out of 3= 3C2= 3

Ways to take 1 white marble out of 4= 4C1= 4

Ways to take 1 purple  marble out of 3= 3C1= 3

Then the probability would be: 4*3*4*3/ 2002= 144/2002= 72/1001