Lesson 3

In Try This 3, you may have noticed that the  column and the total number of possible permutations are the same. This formula provides you with a way to calculate the permutations without the need for tree diagrams or lists. You will discover that the formula can be used to solve a variety of problems in Self-Check 1.

Self-Check 1

1. In how many ways can the president, vice-president, and secretary of the student council be selected from 30 people? Leave your answer in factorial form. Answer
2. How many 4-letter permutations can be formed from the word travel? State your answer in factorial notation and then evaluate. Answer
3. Consider the NHL playoffs. There are 15 teams in the Western Conference.
   
   
   
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   In the quarterfinals, the first-place team plays the eighth-place team, the second-place team plays the seventh-place team, the third-place team plays the sixth-place team, and, finally, the fourth-place team plays the fifth-place team.
   
   
   Western Conference Quarterfinal
   Playoff Format
   
   1st Place vs. 8th Place
   2nd Place vs. 7th Place
   3rd Place vs. 6th Place
   4th Place vs. 5th Place
   
   
   
   1. In how many ways can the top eight positions be filled? Answer
   2. Does it matter in which order you placed the teams—in other words, do you have to fill the first-place team first, the second-place team second, and so on? Answer
   3. Represent your solution using factorial notation. Answer