Question 1201071
.
123 ("year-11") students chose the courses they wanted at the school prom dinner. 
75 chose a starter, 106 chose a main course and 81 chose a dessert. 
67 chose a main course and dessert, 
64 chose a starter and a main course 
while 49 chose a starter and dessert. 
Everybody ordered at least one course. 
Find the probability that a student chosen at random chose all three courses
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<pre>
The number of all students who chose all three cources is

    123 - (75 + 106 + 81 - 67 - 64 -49) = 41


according to the Inclusion-Exclusion principle.


Therefore, the probability that a student chosen at random chose all three courses is

    {{{41/123}}} = {{{1/3}}}.    <U>ANSWER</U>
</pre>

Solved.


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On inclusion-exclusion principle, &nbsp;see this Wikipedia article


https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle



To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;see the lessons


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Advanced-probs-counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Advanced problems on counting elements in sub-sets of a given finite set</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Challenging-problems-on-counting-elements-in-subsets-of-a-given-finite-set.lesson>Challenging problems on counting elements in subsets of a given finite set</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Selected-problems-on-counting-elements-in-subsets-of-a-given-finite-set.lesson>Selected problems on counting elements in subsets of a given finite set</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Inclusion-Exclusion-principle.lesson>Inclusion-Exclusion principle problems</A> 


in this site.



Happy learning (!)