A survey of 1,076 tourists visiting Orlando was taken. Of those surveyed: 297 tourists had visited LEGOLAND 275 tourists had visited Universal Studios 85 tourists had visited both the Magic Kingdom and LEGOLAND 88 tourists had visited both the Magic Kingdom and Universal Studios 73 tourists had visited both LEGOLAND and Universal Studios 34 tourists had visited all three theme parks 95 tourists did not visit any of these theme parks How many tourists only visited the Magic Kingdom (of these three)

129 tourists

Step-by-step explanation:

Let 'A' represent the tourists that visited LEGOLAND, let 'B' represent the tourists that visited Universal Studios, and let 'C' represent the tourists that visited Magic kingdom

The total number of tourists, n = 1,076

The number of tourist surveyed that visited only LEGOLAND = A∩B'∩C' = 297 tourist

The number of tourist that visited only Universal studios, B∩A'∩C' = 275 tourist

The number of tourist that visited both the Magic Kingdom and LEGOLAND, A ∩ B' ∩ C = 85 tourist

The number of tourist that visited both the Magic Kingdom and Universal Studios, A' ∩ C ∩ B = 88 tourists

The number of tourist that visited both the LEGOLAND and Universal Studios, A ∩ B ∩ C' = 73 tourist

The number of tourist that visited all three theme parks, A ∩ B ∩ C = 34 tourist

The number of tourists that did not visit any of these theme parks = 95 tourists

In set theory, we have for three sets

A ∪ B ∪ C = A∩B'∩C' + B∩A'∩C' + C∩A'∩C' + A ∩ B' ∩ C + A' ∩ C ∩ B + A ∩ B ∩ C' + A ∩ B ∩ C

A ∪ B ∪ C = 1,076 - 95 = 981

∴ The number of tourists that only visited Magic Kingdom, 'C∩A'∩C' ', is given as follows;

C∩A'∩C'  = A ∪ B ∪ C - (A∩B'∩C' + B∩A'∩C' + A ∩ B' ∩ C + A' ∩ C ∩ B + A ∩ B ∩ C' + A ∩ B ∩ C)

∴ C∩A'∩C' = 981 - (297 + 275 + 85 + 88 + 73 + 34) = 129

The number of tourists that only visited the Magic Kingdom, C∩A'∩C' = 129 tourist

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680