Question 1090293
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A bag contains 4 red, 2 white and 3 blue balls. If two balls are chosen at {{{highlight(cross(rand))}}} random without replacement, 
find the probability that the balls are of the same {{{highlight(cross(colour))}}} color.
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<pre>
There are  {{{C[4]^2}}} = {{{(4*3)/(1*2)}}} = {{{12/2}}} = 6 combinations to choose two red balls.


There are  {{{C[2]^2}}} = 1 combination to choose two white balls.


There are  {{{C[3]^2}}} = {{{(3*2)/(1*2)}}} = {{{6/2}}} = 3 combinations to choose two blue balls.


Thus there are 6 + 1 + 3 = 10 combinations to choose two balls of the same color.


The entire space of events is  {{{C[4+2+3]^2}}} = {{{C[9]^2}}} = {{{(9*8)/(1*2)}}} = {{{72/2}}} = 36 combinations to choose two balls from the bag containing 4 + 2 + 3 = 9 balls.


Therefore, the probability that the balls are of the same color is  {{{10/36}}} = {{{5/18}}}.
</pre>

Solved.


About combinations and about these magic numbers {{{C[n]^k}}} you can read from the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Combinatorics: Combinations and permutations</U>". 


Also see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-Combinations.lesson>Elementary Probability problems related to combinations</A> 

from the same online textbook.