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: