Suzan sees a bag of marbles, she grabs a handful at random. she has seen a bag containing four red marbles, four green ones, two white ones, and two purple ones. she grabs eight of them. find the probability of the following event, expressing it as a fraction in lowest terms. hint [see example 1.] she does not have all the red ones.

The answer to this question would be: 85/99

In this question, Suzan is taking 8 marble from a bag containing 4 red marbles, 4 green ones, 2 white ones, and 2 purple ones. The total marble in the bag should be: 4+4+2+2= 12. The question is how much the probability to get <4 red marble. In this question, the green, white and purple is not specified so you can join them into not red group. It will be easier to find the probability of "have all the red one" which mean Suzan take 4 red marble and 4 not-red marble

Ways to take 8 marble out of 12=12C5= 12!/4!8!= 495
Ways to take 4 red marble out of 4= 4C4= 1
Ways to take 4 not red marble out of 8= 8C4= 8!/4!4!= 70

Probability to have all the red ones= 1*70/495= 14/99
Then the probability does not have all the red ones= 99/99 - 14/99= 85/99