2020 is a leap year, so there are 366 days from January 1, 2020 to December 31, 2020.

2024 is a leap year, so it has 366 days.

The hour hand moves 30 degrees in 1 hour (360 degrees / 12 hours).

The minute hand moves 6 degrees per minute. In 15 minutes, it moves 15 * 6 = 90 degrees.

The number of different 4-digit PIN codes is P(10, 4) = 10! / (10-4)! = 5040.

The number of 4-digit PIN codes is 10^4 = 10000.

The number of different 4-digit PIN codes is P(10, 4) = 10! / (10-4)! = 5040.

The number of ways is C(5, 2) * C(4, 2) = 10 * 6 = 60.

The number of ways to choose 3 letters from 'APPLE' (considering 'P' is repeated) is C(5, 3) = 10.

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 hands of a clock overlap 11 times in a 12-hour period.

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.