Training Camp (cont 2)

Thinking back to questions from Lessons 2A and 2B, you may think intuitively of another way to solve Example 1 - the Fundamental Counting Principle.

You now have two ways to approach the same question. When you solve permutation problems, making connections between solving methods is important to ensure you solve both correctly and efficiently. In the swim race problem, both methods are feasible. However, consider another example:

Cassy is running a marathon with 59 other competitors. Assuming everyone has an equal chance of winning, how many ways can the first 40 runners finish?

If you use the Fundamental Counting Principle, you must multiply 40 tasks! In this case, it is more efficient to use the _n P _r formula; . Often, your choice of method is determined by the size of the group from which you are choosing.

 

 

You have learned that the Fundamental Counting Principle is useful for small groups and the _n P _r formula is useful for large groups. What happens if the group is very large? Recall from Lesson 2B that the TI-84 calculator cannot work with factorials greater than 69. In this case use the _n P _r function on your calculator. It mimics the calculations in the formula .

The next example shows how to evaluate permutations using a calculator. As you read the example, complete the steps on your calculator . Contact your teacher if you have any difficulty following this example with your calculator.