Estimate the number of personally constructed greeting cards possible at a machine if there are 12 designs, 30 messages, 18 closings, and 10 different paper stocks on which to print the card. Indicate how you made your estimate. How valid was your estimate?
To estimate the number of personally constructed greeting cards possible at a machine with given parameters, we need to calculate the number of possible combinations for each element (designs, messages, closings, and paper stocks) and then multiply them together.
1. Number of designs: If there are 12 designs, you can choose any one of them. Hence, there are 12 possibilities for designs.
2. Number of messages: With 30 different messages available, you can select any one of them. So, there are 30 possibilities for messages.
3. Number of closings: Similarly, with 18 different closings, you can choose any one of them. Thus, there are 18 possibilities for closings.
4. Number of paper stocks: With 10 different paper stocks, you have the choice of selecting any one of them. Therefore, there are 10 possibilities for paper stocks.
To estimate the total number of possible combinations, we multiply the number of possibilities for each element:
12 designs × 30 messages × 18 closings × 10 paper stocks = 64,800 possible combinations
This estimate assumes that you can choose any combination of designs, messages, closings, and paper stocks independently.
Validity of the estimate:
The estimate is valid if all the assumptions are correct. If there are any constraints or dependencies between the elements (e.g., certain designs can only be combined with specific messages), then the actual number of combinations would be different. So, it's essential to ensure that the assumptions match the actual scenario to make the estimate valid.