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danc
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Word Problems book, chapter 6, p. 116-117

by danc Fri Nov 14, 2014 1:04 am

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!
danc
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Re: Word Problems book, chapter 6, p. 116-117

by danc Fri Nov 14, 2014 10:05 pm

Ok, I'm looking over this again and I think I might have figured it out. The first question asks for the number of possible seating arrangements, while the other two (the second example question and the check-your-skills question) only ask for the number of possible combinations of selections, which means order of selection does not matter.

In other words, with seating arrangements, you can have persons A, B and C, or B, A and C as two separate possibilities. But when finding possible groups, a group of persons A, B and C is the same as a group of persons B, A and C, so that only counts as one group, and thus, the difference in solving method.

Is that accurate?
tommywallach
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Re: Word Problems book, chapter 6, p. 116-117

by tommywallach Sat Nov 15, 2014 4:19 pm

Hey Dan,

Yep, you totally nailed it.

In seating "arrangements," it is different if you have Steve in one seat and Dan in another, or Dan in the first seat and Steve in the second.

On a team, there's no inherent reason why having Steve then Dan is different from having Dan then Steve (unless the question introduces positions, but that would be very clear in the prompt).

-t