Combinatorics

Step 1: Understanding the selection process
We have three categories of items: - 6 alike fruits, - 7 alike vegetables, - 8 alike biscuits. We need to determine the number of ways to select at least one item from each category. Step 2: Finding possible selections from each category
Since the items in each category are identical, selecting any number from each category corresponds to choosing a subset. For each category: - The number of ways to select at least one fruit: (choose from 1 to 6). - The number of ways to select at least one vegetable: (choose from 1 to 7). - The number of ways to select at least one biscuit: (choose from 1 to 8). Step 3: Applying the multiplication principle
Since the selections from each category are independent, the total number of ways is given by: Step 4: Conclusion
Thus, the total number of ways to make a selection while ensuring at least one item from each category is: