1. 12P3 = 12! / (12-3)! = 12! / 9! = 12 × 11 × 10 = 1320
2. 12C3 = 12! / (3! × (12-3)!) = 12! / (3! × 9!) = (12 × 11 × 10) / (3 × 2 × 1) = 220
3. 20P2 = 20! / (20-2)! = 20! / 18! = 20 × 19 = 380
4. 20C2 = 20! / (2! × (20-2)!) = 20! / (2! × 18!) = (20 × 19) / (2 × 1) = 190
5. 9P1 = 9! / (9-1)! = 9! / 8! = 9
6. 9C1 = 9! / (1! × (9-1)!) = 9! / (1! × 8!) = 9
7. 9P9 = 9! / (9-9)! = 9! / 0! = 9! = 362880
8. 9C9 = 9! / (9! × (9-9)!) = 9! / (9! × 0!) = 1
9. 9P0 = 9! / (9-0)! = 9! / 9! = 1
10. 9C0 = 9! / (0! × (9-0)!) = 9! / (0! × 9!) = 1
II.
1. Set up: 15C10
Therefore, there are 3003 different ways of selecting ten players that will be in the relay game from a 15 person team.
2. Set up: 5P4
Therefore, there are 120 different ways to use the digits 2, 4, 1, 3, and 8 in a four-digit lock.
3. Set up: 25C5
Therefore, there are 53130 different ways of selecting five from 25 applicants.
4. Set up: 13P2
Therefore, there are 156 different ways of choosing a captain and co-captain from a team of 13 volleyball players.
Parent Tip: Review the logic above to help your child master the concept of combination permutation worksheet.
