Combination & Permutation Anagram

[mark]

I just reviewed the anagram strategy for combination and permutation problems and I'm having problems identifying when order matters or when it doesn't from the word problems. I understand the strategy but I'm having difficulty applying it because I'm not translating the problems correctly. In some problems, I think order doesn't matter when in fact it does and vice versa. Can you suggest a clearer method that identifies when order does/does not matter for the anagram strategy?

[esledge]

Mark, for me, a question that works better than "Does order matter?" is "Is there anything different about these people/things?" If the people/things are different, then assign a different letter to them in the anagram word.

Examples:

5 people are to be seated in a row of seats on an airplane that has an aisle with 3 seats on either side. How many ways can they be seated? Clearly, there is something different about the seats--an aisle seat is different from a window seat, which is different from the middle seat, and left side is different from right side. (Order matters) One solution: Set up a grid with 6 positions (the seats), give the 5 people different/distinct letters A-E, and call the empty seat N. Anagram word is thus ABCDEN. Ways to shuffle these letters? 6!/1!1!1!1!1!1! = 6!

5 people will travel from city A to city B, 3 by plane and 2 by train. How many different ways can the group of 5 divide themselves between the two modes of transportation? It is different to travel by plane than it is to travel by train, so we should assign different letters (P and T) to them in our anagram word. ("Order" matters when it comes to choice of vehicle.) All the people on the train are the same, as seats are not relevant. Likewise for the plane travelers. (Order doesn't matter within each vehicle.) One solution: Set up a grid with 5 people, and the anagram word will represent the transportation for those people: PPPTT. Ways to shuffle these letters? 5!/3!2! = (5)(4)(3!)/3!2! = (5)(4)/(2) = 10.