Permutations and Combinations Easy Level

6 different letters → 6! = 720

Trap: 5,040 is 7!.

Answer: 720

7 letters with L twice and O twice

7! ÷ (2! × 2!) = 5,040 ÷ 4 = 1,260

Trap: 2,520 divides for only one repeated letter.

Answer: 1,260

9 letters: M, T, E each twice

9! ÷ (2! × 2! × 2!) = 3,62,880 ÷ 8 = 45,360

Trap: 3,62,880 ignores the repeats.

Answer: 45,360

Each handshake is a pair: 10C2 = 45

Trap: 90 counts each handshake twice.

Answer: 45

Lines joining vertices = 10C2 = 45

Minus the 10 sides = 35

Trap: 45 includes the sides.

Answer: 35

Each line uses a pair: 12C2 = 66

Trap: 220 counts triangles (12C3).

Answer: 66

Choose 3 points: 10C3 = 120

Trap: 720 treats the order of vertices as different.

Answer: 120

9 × 8 × 7 = 504

Trap: 729 allows repeats; 84 only chooses the digits.

Answer: 504

Each place has 5 choices: 5³ = 125

Trap: 60 forbids repeats.

Answer: 125

Different roles, so order matters: 11 × 10 = 110

Trap: 55 treats the two posts as the same.

Answer: 110