The first digit can be any of 10 digits, the second can be any of 9, the third can be any of 8, and the fourth can be any of 7. Total = 10 * 9 * 8 * 7 = 5040.

Each digit can be any of the 10 digits (0-9), so the total number of PINs is 10^4 = 10000.

The number of 4-digit PINs is P(10, 4) = 5040.

The number of ways to choose 2 from 5 is C(5, 2) = 10.

The number of ways to arrange 5 people is 5! = 120.

The number of arrangements of 4 different colored balls is 4! = 24.

The number of ways to distribute 4 prizes among 10 students is 10P4 = 10! / (10-4)! = 5040.

The number of arrangements of 6 people is 6! = 720.

The number of arrangements of the letters in 'BOOK' is 4! / 2! = 12.

The number of arrangements of the letters in 'MATH' is 4! = 24.

The number of ways to select 2 boys from 5 is C(5, 2) and 2 girls from 5 is C(5, 2). Total = C(5, 2) * C(5, 2) = 10 * 10 = 100.

The number of ways is 5C2 * 6C3 = 10 * 20 = 200.

The number of ways is 5C2 * 7C3 = 10 * 35 = 350.

The number of ways is 8C2 * 6C3 = 28 * 20 = 560.

The number of ways to select 2 boys from 5 is 5C2 and 3 girls from 7 is 7C3. Total = 5C2 * 7C3 = 10 * 35 = 350.

The number of ways to choose 2 from 5 is C(5,2) = 10.

The number of ways to select 2 students from 5 is given by 5C2 = 10.

The number of ways to select 2 from 8 is C(8, 2) = 28.

The number of ways to select 3 books from 10 is given by 10C3 = 120.

The number of ways to arrange 5 people is 5! = 120.

The number of ways to choose 3 from 7 is C(7, 3) = 35.

The number of arrangements of 3 distinct balls is 3! = 6.

Each gift can go to any of the 5 children, so the total ways = 5^3 = 125.

The number of ways to award 3 trophies to 5 students is given by P(5,3) = 5! / (5-3)! = 60.

The number of ways to choose 3 balls from 8 is given by 8C3 = 56.

The number of ways to award 3 prizes is P(10, 3) = 720.

The number of arrangements is 5! / (3! * 2!) = 10.

The number of ways to select 3 students from 10 is given by 10C3 = 120.

The number of arrangements of 4 distinct flags is 4! = 24.

The number of ways to choose 4 fruits from 6 is C(6, 4) = 15.