Three research departments have 7, 10, and 6  members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done?

A survey of 1,152 tourists visiting Orlando was taken. Of those surveyed: 274 tourists had visited the Magic Kingdom 252 tourists had visited LEGOLAND 263 tourists had visited Universal Studios 84 tourists had visited both the Magic Kingdom and LEGOLAND 52 tourists had visited both the Magic Kingdom and Universal Studios 56 tourists had visited both LEGOLAND and Universal Studios 34 tourists had visited all three theme parks How many tourists had not visited any of these three theme parks?

Of 45 members of the Campus Club, 27 had camped at Yellowstone, 23 had camped at Yosemite, and 18 had camped at both. How many had camped at neither?

Part Il: The University board plans to assign a new assistant coach among 5 team sports based on their perfomance in the last UAAP season. The following table shows the points earned by each team and their respective coaches and trainers Basketball Volleyball Swimming Badminton Track & Field Foints Number of trainers 360 290 400 320 380 10 Compute for the Huntington-Hil number for each team. To which team should the additional assistant coach be assigned based on Huntington Hill number?