Question

Consider the three restaurants Panera, Olive Garden, and Red Robin. A survey of 710 customers finds that the numbers of customers who like each restaurant are as follows:

304, Panera
210, Olive Garden
380, Red Robin
140, Panera and Olive Garden
136, Olive Garden and Red Robin
110, Panera and Red Robin
81, all three restaurants

How many of the surveyed customers like EXACTLY ONE of these restaurants?
customers

Answer 1

Solution:
To determine no. of customer surveyed like exactly one of these restaurants
No. of Customer like(Panera) + No. of Customer like(Olive Garden) + No. of Customer like(Red Robin) – 2*No. of Customer like(Panera n Olive Garden) – 2*No. of Customer like(Panera n Red Robin) – 2*No. of Customer like(Olive Garden n Red Robin) + 3*No. of Customer like(Panera n Olive Garden n Red Robin) = 304 + 210 + 380 - 2*140 - 2*136 - 2*110 - 3*81 = 304 + 210 + 380 - 280 - 272 - 220 + 243 = 365
So 365 of the surveyed customers like exactly one of these restaurants.