SOLUTION: please help me. There are 6 black marbles, 6 white marbles, and 7 red marbles in a bag. If five marbles are chosen at random, find the probability that there will be two black, two

Algebra ->  Permutations -> SOLUTION: please help me. There are 6 black marbles, 6 white marbles, and 7 red marbles in a bag. If five marbles are chosen at random, find the probability that there will be two black, two      Log On


   

Question 1124456: please help me. There are 6 black marbles, 6 white marbles, and 7 red marbles in a bag. If five marbles are chosen at random, find the probability that there will be two black, two white, and one red marble.
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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In all, there are  6 + 6 + 7 = 19 marbles.


The probability in this case is the ratio, whose denominator is  C%5B19%5D%5E5, and the numerator is the product


    C%5B6%5D%5E2.C%5B6%5D%5E2.C%5B7%5D%5E1.

Here the symbols  C%5Bn%5D%5Em  denotes the number of combinations of  n  items taken  m  at a time.

When you are given such problem,  it is assumed that you know what the combinations are and how to calculate these numbers.

On combinations,  see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Math circle level problem 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.