The original text isn't in English, so I can't give you that.
Some of the helpers here know other languages, at least to some degree, so don't be shy about posting the original text (along with which language it is).
There are 9 reds, 8 blues, 10 whites and 14 greens, total of 41. I should count, how many possible groups can I get, when there can be one or more in a group (so there can be a group of one and a group of 40? :grin
. If there are two same colours in a group, then there has to be one another colour too (so there can't be a group of 2 reds for example).
If I'm understanding this, you have forty-one items, in the given sets of interchangeable items (for instance, one red marble is just the same as another red marble). You are needing to find the numbers of distinguishable groups which can be formed from these sets of items. You have the following rules for the distinguishable groups:
. . .a. The groups may have any number of items, between one and forty-one.
. . .b. If any group has two of the same colour, then it must also have at least one of another colour.
I think you'll need to work by cases.
Case 1: One marble only. There are four colours, so how many
distinguishable groups of one item can you form?
Case 2: Two marbles. You know that you can't have a group of two of the same colour, because this would automatically (by Rule (b)) force the addition of at least one other marble. So you can only have groups of two of differing colors. Since this means "groups of two, being one each of two different colours", you effectively have 1 red, 1 blue, 1 white, and 1 green. How many groups can you form from these?
Case 3: Three marbles. You have two different sub-cases: two of one colour, plus one of another; or three different colours. You can't have all three of one colour, because (by Rule (b) again), you'd then immediately have to add at least one of a different colour. So you have:
Case 3-i: Two of one colour, plus one of another. How many ways can you do this?
Case 3-ii: Three, each of a different colour. How many ways can you do this?
And so forth. At some point, you may note a pattern, which may simplify things. If not, power through!