I am confused by the explanations for the two different methods used to solve the example question at the bottom of p. 116 and the check-your-skills question (#5) on p. 117.
Can you explain the inherent difference between seats on a shuttle and spots on a team? The book says "the three seats on tn the shuttle were considered different" but that spots on a team are not unique, that they are all exactly the same.
In what way is that true?
One can easily (and literally) view a spot on a team as equivalent to a seat on a bus, and one can easily view a seat on a bus as a spot on a team. Even if each seat were designated as different (one as a recliner, one as a folding chair and one as a bar stool), the number of possible combinations will be the same, because whichever person takes the recliner, he or she is no longer a candidate to take the other two. And if the seats are all identical, the person who takes the first seat will not be a candidate for the other two seats. So what is the difference?
The spots on the team are exactly the same. In fact, basketball teams have exactly one seat on the sideline for each player on the team. Thus, if there are five spots available on the team, that is the same as having five seats available on a shuttle.
So, what exactly is the inherent difference in the two entities that necessitate the different methods to solve the problems?
Essentially, in one question we have three seats available and seven candidates to fill them. In another question, we have five spots available and eight candidates to fill them. How are those different questions (besides the numbers)?
Thanks!