Question

in a group of 80 people 43 like coffee, 52 like tea and each person like at least one of the two drinks. how many people like both tea and coffee​

Answer 1

Answer:

15 peoples

Step-by-step explanation:

people like coffee = 43

people like tea =52

43+52=95

total people =80

95-80=15

=15 people like both

Answer 2

Answer:

The number of people who like both coffee and tea is 15.

Step-by-step explanation:

• When the two given sets A and B are finite sets and not disjoint sets,  then $A \cup B$ and $A \cap B$ are finite and both are related through a theorem called inclusion–exclusion principle, given by  

       $n(A \cup B) = n(A) + n(B) - n(A \cap B)$

• where the number of elements in union set, $n(A \cup B)$ includes n(A) and n(B) and excludes $n(A \cap B)$, since the elements in intersection were counted twice.

Given the number of people who like coffee, n(C)=43

Number of people who like tea, n(T)=52

The total number of people in a group, $n(C\cup T) = 80$

Using the formula,

$n(C\cup T)=n(C)+n(T)-n(C\cap T)$

Substituting the values,

$80=43+52-n(C\cap T)$

$\implies n(C\cap T) =95-80=15$

Thus, the number of people who like both coffee and tea is 15.

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