Permutations and Combinations Easy Level

Choosing only: 8C3 = 56

Trap: 336 also arranges them.

Answer: 56

7P4 = 7 × 6 × 5 × 4 = 840

Trap: 35 only chooses the books.

Answer: 840

Circular arrangements of n = (n − 1)!

5! = 120

Trap: 720 counts rotations as different.

Answer: 120

Circular: 6! = 720

A necklace can be flipped, so divide by 2: 360

Trap: 720 treats clockwise and anticlockwise as different.

Answer: 360

nCr = nC(n − r), so 8 + 6 = n

n = 14

Answer: 14

n(n − 1) = 90 = 10 × 9

n = 10

Answer: 10

Each letter has 4 choices: 4⁵ = 1,024

Trap: 625 = 5⁴ gives each box a choice of letter.

Answer: 1,024

2 choices each: 2⁶ = 64

Trap: 12 adds instead of multiplying.

Answer: 64

Vowels A, U, E as one block + D, G, H, T, R → 6 units: 6! = 720

Vowels inside the block: 3! = 6

720 × 6 = 4,320

Trap: 720 forgets to arrange the vowels.

Answer: 4,320

Fix S; arrange C, H, O, O, L: 5!/2! = 60

Trap: 120 forgets the repeated O.

Answer: 60