word problems pg 105 anagrams grid

[csc7]

I have a question about the example question on pg 105 of the 3rd edition word problems book. So it's saying that 7 people board a shuttle, but there's only 3 seats. In order to solve, the book says it's 7!/4!, but why the 4. I thought there was only 3 seats. Wouldn't it be 3! Or are they including someone standing in the equation, which would make it 4! then. I just need a clarification about this, thanks!

[tommywallach]

Hey Chang,

You know, I'm not a fan of the anagram grid. I do this with the slots method, which works like this:

1. Find the # of slots (the # of decisions you get to make)
2. Input the number of choices at each decision point
3. Find out if order matters or not (or both)
4. Multiply all the slots together, then divide by the # of slots factorial wherever order doesn't matter.

In this case:

1. There are three slots, so I write _ _ _ on my paper.
2. There are seven choices for the first slot, six for the second, five for the third, so I write 7 6 5
3. Order matters here (because it asks for arrangements), so we simply multiply 7 * 6 * 5 = 210.

Tada!

-t

P.S. But in answer to your question, with the anagram grid method, you have to divide by 4! because you're only using 3 of the 7 seats, so you have to "remove" the combinations created by the other 4 seats. My method is better though. : )