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sineoko [7]
3 years ago
13

When a group of colleagues discussed where their annual retreat should take​ place, they found that of all the​ colleagues: 17 w

ould not go to a​ park, 24 would not go to a​ beach, 13 would not go to a​ cottage, 8 would go to neither a park nor a​ beach, 3 would go to neither a beach nor a​ cottage, 2 would go to neither a park nor a​ cottage, 1 would not go to a park or a beach or a​ cottage, and 8 were willing to go to all three places. What is the total number of colleagues in the​ group?
Mathematics
2 answers:
Vilka [71]3 years ago
7 0
To find the answer look for opinions where 1 person can't have multiple.

Add them all up and you'll get your answer, there are 33 total colleagues in the group.
NARA [144]3 years ago
7 0
We're assuming e.g. the two that won't go to P (park) or C (cottage) includes the one that won't go anywhere.

Let's call the three rings of the Venn diagram P,B,C.
 
We'll label the eight regions like PB\bar{C}, here meaning in P, in B, not in C.


1 would not go to a park or a beach or a​ cottage

\bar{P}\bar{B}\bar{C} = 1

8 would go to neither a park nor a​ beach.  We have to take away the one guy who won't go anywhere to find out how many go just to college.

8 = \bar{P}\bar{B}\bar{C} + \bar{P}\bar{B}C 

\bar{P}\bar{B}C=8-1=7 

3 would go to neither a beach nor a​ cottage,

P\bar{B}\bar{C}=3-1=2 

<span>2 would go to neither a park nor a​ cottage, 
</span>
\bar{P}B\bar{C} = 2-1=1 

<span>17 would not go to a​ park

</span>17 = \bar{P}\bar{B}\bar{C} + \bar{P}\bar{B}{C} + \bar{P}{B}\bar{C} + \bar{P}{B}{C}= 1 + 7 + 1 + \bar{P}{B}{C}

\bar{P}{B}{C}=8

<span>24 would not go to a​ beach

</span>{P}\bar{B}{C}=24 - 1 - 7 - 2 = 14

13 would not go to a​ cottage
 
{P}B\bar{C}=13 - 1 -2 - 1= 9

8 were willing to go all three places.

{P}BC= 8

Adding them all up,

8 + 9+ 14+ 8 + 1 + 2 + 7 + 1 = 50


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