# The product principle

## Homework Statement

In how many different ways can the top two positions be filled in a table tennis competition of 7 teams?
How many 3-digit numbers can be formed using the digits 2, 3, 4, 5, and 6:
a) as often as desired? b) once only?

## The Attempt at a Solution

I can find the solution using the long way, but I'm wondering if there is a more logical and mathematical way to approach these equations?

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you know permutations and combinations?

I got the first equation, and the b) section of equation 2, but how about a)? I'm confused by what they are asking.

yes...that's what I used to solve for equation 1, and b), but a's wording is slightly confusing :p

nrqed
Homework Helper
Gold Member
yes...that's what I used to solve for equation 1, and b), but a's wording is slightly confusing :p
You may use the same digit twice or even three times (like 665 or 666). That's all they mean.
So how many choices do you have for the first digit? how many choices for the second? How many for the third? Multiply those three numbers and you are done.

Oh Ok. So just to clarify things, each number could be used five times...therefore 5^3...and when each value is used once, 5x4x3....which suggests that in the first box, any value of the series could be used, in the second box, what's left over, etc...is my explanation correct? If you have a better one, feel free to share it ;p.

HallsofIvy