Question

When a group of colleagues discussed where their annual retreat should take​ place, they found that of all the​ colleagues: 12 would not go to a​ park, 10 would not go to a​ beach, 12 would not go to a​ cottage, 8 would go to neither a park nor a​ beach, 9 would go to neither a beach nor a​ cottage, 5 would go to neither a park nor a​ cottage, 4 would not go to a park or a beach or a​ cottage, and 5 were willing to go to all three places. What is the total number of colleagues in the​ group?

Answer 1

Given that 4 people would not go to a park or a beach or a​ cottage.

Number of people that will go to neither a park nor a​ cottage but will go to a beach = 5 - 4 = 1.

Number of people that will go to neither a beach nor a​ cottage but will go to a park = 9 - 4 = 5

Number of people that will go to neither a park nor a​ beach but will go to a cottage = 8 - 4 = 4


Number of people that will not go to a​ cottage but will go to a beach or a park = 12 - 5 - 1 = 6

Number of people that will not go to a​ beach but will go to a cottage or a park = 10 - 5 - 4 = 1

Number of people that will not go to a​ park but will go to a beach or a cottage = 12 - 4 - 1 = 7

Number of people willing to go to all three places = 5

Therefore, total number of colleagues = 4 + 1 + 5 + 4 + 6 + 1 + 7 + 5 = 33