1. ## sequence

if we make a sequence selecting three elements from three different elements {1,2,3} and we permit overlapped element for the sequence, then the total, number os sequences is..... if we do not take into account the order, the total number of the selections is.....

2. ## Re: sequence

The above formulas should be useful. I will assume "overlapped element" means repetition is allowed in this case.

Hence,
If we do take account the order, we use Permutations: Order Matters, Repetition Allowed.
If we don't take account the order, we use Combinations: Order doesn't Matter, Repetition Allowed.

Can you finish?

3. ## Re: sequence

Originally Posted by provasanteriores
if we make a sequence selecting three elements from three different elements {1,2,3} and we permit overlapped element for the sequence, then the total, number os sequences is..... if we do not take into account the order, the total number of the selections is.....
That must be a very poor translation. It makes not sense whatsoever.
Making a selection of three from three possible kinds is just that, done in $3^3=27$ ways.
However, elements of sequences do not overlap. There must be another meaning there.

Do you mean something like: We have a supply of red, blue, and yellow balls. Select three???
EXAMPLES: $RBY$, $BBY$, $RYR$ or $BBB$