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A survey of 545 adults aged 18-24 years old was conducted in which they were asked what they did last Friday night. How many 18-24 year olds (of these three activities) only ate pizza last Friday night?

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Final answer:

There were 149 individuals aged 18-24 who only hung out with friends last Friday night.

Step-by-step explanation:

Let's denote the sets as follows:

- A : Those who watched TV

- B : Those who ate pizza

- C : Those who hung out with friends

We are given the following information:

|A| = 186

|B| = 185

|A ∩ B ∩ C'| = 38

|A ∩ C ∩ B'| = 36

|B ∩ C ∩ A'| = 35

|A ∩ B ∩ C| = 37

|U| = 545 (where U is the universal set)

And we know that |A' ∩ B' ∩ C'| = 77 (those who did not do any of these activities).

We can use the principle of inclusion-exclusion to find the number of people who only hung out with friends:

|A ∩ B' ∩ C| = |A| - |A ∩ B ∩ C'| - |A ∩ C ∩ B'| + |A ∩ B ∩ C|

Substitute the given values:

|A ∩ B' ∩ C| = 186 - 38 - 36 + 37

|A ∩ B' ∩ C| = 149

So, there were 149 individuals who only hung out with friends last Friday night.

Your complete question is: A survey of 545 adults aged 18-24 year olds was conducted in which they were asked what they did last Friday night. It found: - 186 watched TV - 185 ate pizza - 38 watched TV and ate pizza, but did not hang out with friends - 36 watched TV and hung out with friends, but did not eat pizza - 35 hung out with friends and ate pizza, but did not watch TV - 37 watched TV, hung out with friends, and ate pizza - 77 did not do any of these three activities How may 18-24 year olds (of these three activities) only hung out with friends last Friday night?

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