The number of ways to choose 3 letters from 8 is C(8, 3) = 56.

The number of ways to select 3 students from 10 is C(10, 3) = 10! / (3! * (10-3)!) = 120.

The number of arrangements is 6! / (3!) = 20.

The number of arrangements of 'LEVEL' is 5! / (2! * 2!) = 30.

The leap years between 2000 and 2020 are 2000, 2004, 2008, 2012, 2016, and 2020. That makes a total of 6 leap years.

Leap years between 2000 and 2020 are 2000, 2004, 2008, 2012, 2016, and 2020. Total = 5 leap years.

The number of ways to award trophies is P(10, 3) = 10! / (10-3)! = 720.

The number of ways is C(5, 2) * C(6, 3) = 10 * 20 = 200.

The number of ways to award 3 prizes to 5 students is P(5, 3) = 60.

Treat the 2 specific books as one unit. So, we have 3 units to arrange: (2 books together + 2 other books) = 3! * 2! = 12.

The number of ways to arrange 4 different colored balls is 4! = 24.

The number of arrangements of 4 people at a round table is (4-1)! = 3! = 6.

The number of ways to select 4 people from 12 is C(12, 4) = 495.

The number of arrangements of 5 distinct books is 5! = 120.

The number of ways to choose 5 books from 15 is C(15, 5) = 3003.

The number of ways to select and arrange 5 books is 5! = 120.

Each ball can go into any of the 3 boxes, so the total ways = 3^5 = 243.

Treat the 2 letters as one unit, so we have 4 units to arrange: 4! * 2! = 48.

Each prize can go to any of the 3 students, so there are 3^5 = 243 ways.

Each prize can go to any of the 3 students. Therefore, the total ways = 3^5 = 243.

The number of arrangements of 6 different colored balls is 6! = 720.

The number of ways to arrange 6 people in a round table is (6-1)! = 5! = 120.

Treat the two specific people as one unit. Then, we have 5 units to arrange: 5! = 120. The two people can be arranged in 2! ways. Total = 120 * 2 = 240.

Treat the 2 specific books as one unit. Then, arrange 6 units: 6! * 2! = 1440.

The number of ways to form a committee is C(8,3) = 56.

The number of arrangements is 6! / (3!) = 20.

Total Amount = 1200(1 + 0.10)^3 = 1200(1.331) = 1597.20

Total Amount = P(1 + r/n)^(nt) = 1500(1 + 0.04/1)^(1*5) = 1500(1.2166529) = 1824.98

Amount = P(1 + r)^n = 2000(1 + 0.06)^3 = 2000(1.191016) = $2380.03

Amount = P(1 + r)^n = 5000(1 + 0.04)^10 = 5000(1.48024) = $7401.20.