Calculating Resistance in Series and Parallel Lamp Combinations

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The discussion revolves around calculating total resistance for various combinations of five lamps arranged in series and parallel. The formulas for total resistance are correctly identified: for parallel, 1/Rt = 1/R1 + 1/R2 + ... + 1/R5, and for series, Rt = R1 + R2 + ... + R5. However, not all combinations of lamps are valid; only specific arrangements yield meaningful resistance values. The participant acknowledges that combinations like four lamps in parallel and one in series exist, indicating a need for clarification on acceptable configurations. Understanding the limitations of these combinations is crucial for accurate calculations.
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I'm stuck on this homework I need to do but it's for tomorrow and it's very important. Could one of you please answer this? The question is:
There are 10 different combinations that lamps can be arranged if there are 5 of them and you can organise them only in series and only in parallel. The formula for calculating the total resistance in parallel is 1/Rt = 1/R1 + 1/R2 etc until 5. And for series it is Rt = R1 + R2 until R5. Is the formulae for calculating r in series and parallel for all 10 lamp combinations acceptable? Explain your answer.
I know the answer is that not all the combinations are accepted but that's all I know
 
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between having all 5 in parallel and all 5 in series aren't there other combinations, maybe 4 in parallel and 1 in series and so on...
 

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