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The table shows the year in school and the number of years experience for 18 players on a high school soccer team. The coach can choose 2 players to be captains. A captain must be a junior (Jr) or a senior (Sr), and have played on the team for more than 1 year.

Information
,begin bold,Player,end bold,

,begin bold,1,end bold,

,begin bold,2,end bold,

,begin bold,3,end bold,

,begin bold,4,end bold,

,begin bold,5,end bold,

,begin bold,6,end bold,

,begin bold,7,end bold,

,begin bold,8,end bold,

,begin bold,9,end bold,

,begin bold,10,end bold,

,begin bold,11,end bold,

,begin bold,12,end bold,

,begin bold,13,end bold,

,begin bold,14,end bold,

,begin bold,15,end bold,

,begin bold,16,end bold,

,begin bold,17,end bold,

,begin bold,18,end bold,

,begin bold,Year in School,end bold,

Sr

Fr

Jr

So

So

Sr

Sr

Jr

Jr

Fr

Sr

Sr

Sr

So

Jr

Jr

Sr

So

,begin bold,Years on Team,end bold,

1

1

2

2

2

3

4

3

1

1

1

3

4

2

3

1

2

2


Question
How many different captain pairs can the coach choose?

Response area with 1 text input box
The coach can choose
different pairs as captains.

1 answer

To determine how many different pairs of captains the coach can choose, we first need to identify which players are eligible based on the given criteria: being either a junior (Jr) or a senior (Sr) and having played on the team for more than 1 year.

Let's analyze the data provided in the table.

Eligible Players:

  1. Player 1: Sr, 1 year (not eligible)
  2. Player 2: Fr, 1 year (not eligible)
  3. Player 3: Jr, 2 years (eligible)
  4. Player 4: So, 2 years (not eligible)
  5. Player 5: So, 2 years (not eligible)
  6. Player 6: Sr, 3 years (eligible)
  7. Player 7: Sr, 4 years (eligible)
  8. Player 8: Jr, 3 years (eligible)
  9. Player 9: Fr, 1 year (not eligible)
  10. Player 10: Sr, 1 year (not eligible)
  11. Player 11: Sr, 3 years (eligible)
  12. Player 12: Sr, 4 years (eligible)
  13. Player 13: So, 2 years (not eligible)
  14. Player 14: Jr, 3 years (eligible)
  15. Player 15: Jr, 2 years (eligible)
  16. Player 16: Sr, 1 year (not eligible)
  17. Player 17: So, 2 years (not eligible)
  18. Player 18: Sr, 2 years (eligible)

List of Eligible Players:

  • Player 3 (Jr, 2 years)
  • Player 6 (Sr, 3 years)
  • Player 7 (Sr, 4 years)
  • Player 8 (Jr, 3 years)
  • Player 11 (Sr, 3 years)
  • Player 12 (Sr, 4 years)
  • Player 14 (Jr, 3 years)
  • Player 15 (Jr, 2 years)
  • Player 18 (Sr, 2 years)

Total Eligible Players:

We find that there are 9 eligible players.

Choosing 2 Captains:

The formula for choosing 2 players from a group of 9 is given by the combination formula \( C(n, k) \), where \( n \) is the total number of items (players, in this case) and \( k \) is the number of items to choose (2 players).

\[ C(9, 2) = \frac{9!}{2!(9-2)!} = \frac{9 \times 8}{2 \times 1} = 36 \]

Final Answer:

The coach can choose 36 different pairs as captains.