As with permutations, there are often extra conditions placed on the choices to be made. If, in Self-Check 2, the coach had to make choices based on positions, the number of combinations would change. Consider the scenario in Try This 3.
Try This 3
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A hockey coach wishes to choose a first line. The coach has to choose 1 of 5 centres, 1 of 7 right wingers, 1 of 6 left wingers, and 2 of 10 defence players. In how many ways can the coach choose the first line?
Use a table similar to the following table to help solve the problem.
| Position | Centre | Right Wing | Left Wing | Defence | |
| Number of Players to Choose From | 5 | 7 | 6 | 10 | |
| Number on Ice at One Time | 1 | 1 | 1 | 2 | |
| Combination Notation | |||||
| Number of Ways to Fill Each Position | |||||
| Total Number of Ways | total = ?  |
||||
Hemera/Thinkstock
Save your responses in your course folder.
Share 3
With a partner or group, discuss the following questions based on your answer to Try This 3.
- Compare the ways your group determined how the starting line could be formed.
- Of the methods you saw, describe the one that seems most efficient.
If required, save a record of your discussion in your course folder.