Question 1125217
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            The solution by the tutor @math-helper is fine.


            I want to show you different way to solve the last part.



<pre>
There are two ways to get 30:  30 = 10+10+10   and/or   30 = 20 + 5 + 5.

There are no other ways.


In all, there are  {{{C[9]^3}}} = {{{(9*8*7)/(1*2*3)}}} = 84 different groups of three banknotes (without looking the order).


Of these 84 groups, there is only one group containing 3 "tens". It contributes  {{{1/84}}} to the total probability.


Also, there are 9 groups containing (20,5,5) in any order.   

                                    (9 = <U>3 ways to get 20 from the 3 "T"</U>  MULTIPLIED  by <U>3 ways to get the pair (5,5)  from 3 "F"</U>).


                                                                 It contributes  {{{9/84}}} to the total probability.


So, the total probability under the question for this part of the problem is  {{{1/84}}} + {{{9/84}}} = {{{10/84}}} = {{{5/42}}},

which coincides with the answer by the tutor @math-helper.
</pre>

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On Combinations, &nbsp;see 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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and 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>". 



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.