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

Question 1115051: that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms.
She has all the red ones.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
It is very simple problem. Much simpler than you, probably, thought at the beginning.
Your major task is to read the condition attentively to maximally simplify it.

The total number of balls in the bag was initially 4 + 3 + 2 + 1 = 10.

How many ways are there to grab 8 balls from 10 ?  - There are   =  =  = 45 ways.

    It is the full space of events.



In how many ways she may have 4 red balls among those 8 she grabbed? - In   =  =  = 15 ways.

    (just having 4 red, she can complement them by 4 other balls, choosing them arbitrary among 6 remaining balls).



So, the probability under the question is   =  = 33.33%

Solved.

-----------------
On Combinations, see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations

    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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