In a group of 50 patrons, 8 patrons like lattes and espressos, 12 patrons like espressos and cappuccinos, 9 patrons like lattes and cappuccinos, and 5 patrons like all 3 coffee drinks. altogether, 20 patrons like lattes, 28 patrons like espressos, and 19 patrons like cappuccinos. how many patrons don't like any of these coffee drinks? .

a. 9.
b. 4.
c. 3.
d. 7

Let's count how many patrons like only two of these coffe drinks:

1. If 5 patrons like all 3 coffee drinks and 8 patrons like lattes and espressos, then 8-5=3 like only lattes and espressos.

2. If 5 patrons like all 3 coffee drinks and 12 patrons like espressos and cappuccinos, then 12-5=7 like only espressos and cappuccinos.

3. If 5 patrons like all 3 coffee drinks and 9 patrons like lattes and cappuccinos, then 9-5=4 like only lattes and cappuccinos.

Let's count how many patrons like only one of these coffe drinks:

1. For espresso:

a) 5 patrons like all 3 coffee drinks

b) 3 patrons like only lattes and espressos

c) 7 patrons like only espressos and cappuccinos

d) 28 patrons like espressos

Then 28-5-3-7=13 patrons like espressos.

2. For cappuccino:

a) 5 patrons like all 3 coffee drinks

b) 4 patrons like only lattes and cappuccinos

c) 7 patrons like only espressos and cappuccinos

d) 19 patrons like cappuccinos

Then 19-5-4-7=3 patrons like cappuccinos.

3. For lattes:

a) 5 patrons like all 3 coffee drinks

b) 4 patrons like only lattes and cappuccinos

c) 3 patrons like only lattes and espressos

d) 20 patrons like lattes

Then 20-5-4-3=8 patrons like lattes.

Add all numbers that denote one, two or all three drinks patrons:

8+3+13+3+7+4+5=43 patrons that like some of coffee drinks. In total there are 50 patrons, then 50-43=7 patrons don't like any of these coffee drinks.

7 patrons, correct choice is D.

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