Permutation and Combination Worksheets - Free Printable

I'll solve each permutation and combination problem step by step.

Let me work through all 12 problems:

Problem 1: -C(20, 18)
- C(20, 18) = 20!/(18!(20-18)!) = 20!/(18! × 2!)
- C(20, 18) = (20 × 19)/(2 × 1) = 380/2 = 190
- Answer: -190

Problem 2: C(6, 5) × P(8, 1)/3
- C(6, 5) = 6!/(5! × 1!) = 6
- P(8, 1) = 8!/7! = 8
- So we have: 6 × 8/3 = 48/3 = 16

Problem 3: 8 + P(3, 3) - P(2, 2)
- P(3, 3) = 3!/0! = 6
- P(2, 2) = 2!/0! = 2
- Answer: 8 + 6 - 2 = 12

Problem 4: C(3, 1)/P(4, 2)
- C(3, 1) = 3!/(1! × 2!) = 3
- P(4, 2) = 4!/2! = 4 × 3 = 12
- Answer: 3/12 = 1/4 or 0.25

Problem 5: P(8, 2)/(C(5, 3) + 6)
- P(8, 2) = 8!/6! = 8 × 7 = 56
- C(5, 3) = 5!/(3! × 2!) = (5 × 4)/(2 × 1) = 10
- Denominator: 10 + 6 = 16
- Answer: 56/16 = 7/2 or 3.5

Problem 6: 4! + C(61, 60)
- 4! = 24
- C(61, 60) = 61!/(60! × 1!) = 61
- Answer: 24 + 61 = 85

Problem 7: 3P(6, 4)
- P(6, 4) = 6!/2! = 6 × 5 × 4 × 3 = 360
- Answer: 3 × 360 = 1080

Problem 8: -P(9, 3) + C(17, 14)
- P(9, 3) = 9!/6! = 9 × 8 × 7 = 504
- C(17, 14) = C(17, 3) = 17!/(14! × 3!) = (17 × 16 × 15)/(3 × 2 × 1) = 4080/6 = 680
- Answer: -504 + 680 = 176

Problem 9: C(8, 7) - P(5, 1)
- C(8, 7) = 8!/(7! × 1!) = 8
- P(5, 1) = 5!/4! = 5
- Answer: 8 - 5 = 3

Problem 10: -C(4, 3) × P(7, 4)
- C(4, 3) = 4!/(3! × 1!) = 4
- P(7, 4) = 7!/3! = 7 × 6 × 5 × 4 = 840
- Answer: -4 × 840 = -3360

Problem 11: 2! - 11/C(5, 3)
- 2! = 2
- C(5, 3) = 10 (calculated earlier)
- Answer: 2 - 11/10 = 2 - 1.1 = 0.9 or 9/10

Problem 12: 6C(7, 5) + 5P(9, 2)
- C(7, 5) = C(7, 2) = 7!/(5! × 2!) = (7 × 6)/(2 × 1) = 21
- P(9, 2) = 9!/7! = 9 × 8 = 72
- Answer: 6 × 21 + 5 × 72 = 126 + 360 = 486

Final Answer:
1) -190
2) 16
3) 12
4) 1/4 or 0.25
5) 7/2 or 3.5
6) 85
7) 1080
8) 176
9) 3
10) -3360
11) 9/10 or 0.9
12) 486