Permutations and Combinations Exam Pattern Mix

Subtract 2 from each: x′ + y′ + z′ = 9

(9 + 2)C2 = 55

Trap: 136 = 17C2 ignores the minimum.

Answer: 55

Choose: 3C2 × 5C3 = 3 × 10 = 30

Arrange the 5 letters: 5! = 120

30 × 120 = 3,600

Trap: 30 only chooses.

Answer: 3,600

First square: 64; second avoids its row and column: 49

Order does not matter: 64 × 49 ÷ 2 = 1,568

Trap: 3,136 counts each pair twice.

Answer: 1,568

Choose 3 rows and 3 columns: 8C3 × 8C3 = 56 × 56

Match rows to columns: 3! = 6

56 × 56 × 6 = 18,816

Answer: 18,816

All: 4!/2! = 12

Os together: 3! = 6

Not together = 6

Answer: 6

Arrange A, A, I, N: 4!/2! = 12

5 gaps; the four Ss take 4 of them: 5C4 = 5

12 × 5 = 60

Trap: 840 is all arrangements.

Answer: 60

1² + 2² + 3² + 4² + 5² = 55

Trap: 25 counts only the small squares.

Answer: 55

6 lines each way: 6C2 × 6C2 = 15 × 15 = 225

Trap: 170 leaves out the squares.

Answer: 225

6 rights and 4 ups in any order: 10C4 = 210

Trap: 24 multiplies 6 × 4.

Answer: 210

Even places 2, 4, 6 for the women: 3! = 6

Men in places 1, 3, 5, 7: 4! = 24

6 × 24 = 144

Answer: 144