A Permutation Problem I Need To Solve

Hi there folks i hope someone can help with this problem.
Im in the business of making some interchangeable objects and looking for a calculator to assist in working out the total number of permutations or combinations.
(sorry I'm unsure if I'm after number of permutations or combinations, i think its permutations?)
I have seen some tools available on the web but my problem cannot be solved with the tools i have found so far, i will try to explain my problem below and if someone is aware of a tool i can use to solve the e.g. problem and similar problems i will be much appreciative.
I have several parts i need to solve the same problem but below is an e.g. of 1 of my parts.

Eg Part 1
Part 1 is made up of 5 segments and each segment is available in different numbers of variation.
All 5 segments must be in order to make up the part but only 1 option per segment.

Segment 1 is available in 5 Options
Segment 2 is available in 25 Options
Segment 3 is available in 5 Options
Segment 4 is available in 10 Options
Segment 5 is available in 5 Options

How many different parts (or variations of segments) can i make from the available 5 segments using the available number of options per segment?

Thanks in advance for any assistance.

Cheers

Kitacooch said:

Eg Part 1
Part 1 is made up of 5 segments and each segment is available in different numbers of variation.
All 5 segments must be in order to make up the part but only 1 option per segment.
Segment 1 is available in 5 Options
Segment 2 is available in 25 Options
Segment 3 is available in 5 Options
Segment 4 is available in 10 Options
Segment 5 is available in 5 Options
How many different parts (or variations of segments) can i make from the available 5 segments using the available number of options per segment?

Click to expand...

\(\displaystyle (5)(25)(5)(10)(5)=31250\)
This is simple multiplication: SEE HERE.

pka said:

\(\displaystyle (5)(25)(5)(10)(5)=31250\)
This is simple multiplication: SEE HERE.

Click to expand...

Thanks pka, is it really that simple? I was sure it was more complicated than that , but my head hurts trying to think about it.
Ill have to take your word on it mate.

Cheers

So i assume that means the old combination bycicle locks which have 4 segments of 9 have a total combination or (permutation?) of 9X9X9X9 = 6561?

Kitacooch said:

So i assume that means the old combination bycicle locks which have 4 segments of 9 have a total combination or (permutation?) of 9X9X9X9 = 6561?

Click to expand...

Indeed. It is called the multiplicative principle.

Kitacooch said:

So i assume that means the old combination bycicle locks which have 4 segments of 9 have a total combination or (permutation?) of 9X9X9X9 = 6561?

Click to expand...

Permutations are where the order matters and in combinations the order does not matter. In fact it should NOT be called a combination lock but rather a permutation lock!

Thanks pka, my headache is now gone.

Jomo said:

Permutations are where the order matters and in combinations the order does not matter. In fact it should NOT be called a combination lock but rather a permutation lock!

Click to expand...

I would prefer to say permutations are concerned with order, whereas combinations are concerned with content.

To illustrate: Suppose there is a club having thirty members. How many ways can a home-coming committee of three be chosen? How many ways can three officers, Pres., VP, & Secretary be chosen?
One of those is about order & one is about content. Which is which?