SOLUTION: Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing two red marbles, four green ones, three white ones, and two purple ones. She grab

Question 1174469: Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing two red marbles, four green ones, three white ones, and two purple ones. She grabs six of them. Find the probability of the following event, expressing it as a fraction in lowest terms.
She does not have all the red ones.
Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
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Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing
two red marbles, four green ones, three white ones, and two purple ones. She grabs six of them.
Find the probability of the following event, expressing it as a fraction in lowest terms.
She does not have all the red ones.
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There are  2 + 4 + 3 + 2 = 11 marbles, in total.


There are  11-2 = 9 of them, EXCLUDING two red marbles (the set NR = NotRed)


The number of all possible 6-ples is    =  = 462.


If 6-ple does not have all the red ones, it means that this 6-ple is taken from the set of 9 NotRed.


There are    =   = 84 such 6-ples.


The probability under the problem's question is  P =  = .    ANSWER

Solved.

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