Combintorics Question, Guide 5 Chap 10 -Easy Prac. set Q #1

[kpatel986]

Tommy,

Im having a very hard time getting past a concept in the combintorics chap, i can''t tell when something seems indistinguishable or not. For example, with Q#1, there are 2 ways of solving the problem, the slot method and the anagram chart. Although I prefer the slot method, I find it that its very easy to make a mistake with a complicated problem and therefore like the anagram chart method.

Here's the problem: 5 stand-by passengers are waiting for 3 open seats on an airplane flight. in how many different ways can 3 passengers be arranged in these seats?

Usually I would solve this problem by (using the chart method) by deciding if the chosen passengers are distinguishable or not. if they're indistinguishable then the set up would look like this 5!/ (3! * 2!). If they're distinguishable, then it would look like this 5!/ 2!.

- kishan

[tommywallach]

Hey Kpatel,

2 things.

1) I don't use the anagram grid. I hate it. Only slots.

2) "Indistinguishable" is NOT the right way to think about it. The language we use is whether order matters or not. In this case, order matters, because they TOLD you that it was a question of arrangement (another word for order).

So we have three slots, and order matters.

5 * 4 * 3 = 60

If order didn't matter, they would say something like, "How many groups of passengers can go in those three seats." Then, we would divide by the # of slots factorial (this is what you do whenever and wherever order doesn't matter):

5 * 4 * 3 / 3! = 10

Hope that helps!

-t