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.
Answer: 7 patrons, correct choice is D.
