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**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

A man goes to work by train, by taxi or by bus. In how many ways can he arrange his mode of travel for a 6-day week?

-What's the formula and the explanation?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

If it is train or taxi or bus each day then we have:

3 choices the first day

3 choices the second day

all the way down to the 6th day

We use the multiplication rule: 3 * 3 * 3 * 3 * 3 * 3 = 3^6 = 9^3 = 729 ways

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

the multiplication rule is the permutation n^r rule right? so we have 3 modes to choose from and we are choosing 6?

http://www.mathsisfun.com/combinatorics/combinations-permutations.html

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Use n^r, 3 modes and you are choosing them 6 times. Because you have the same 3 choices over and over, you just multiply.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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