Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is :
When selecting one or more identical balls from multiple colors, the number of ways is found by considering the choices for each color independently. For each color, you can choose any number from 0 to the total available. The total ways to choose balls (including selecting none) is calculated by multiplying one more than the count for each color: (10+1) for white, (9+1) for green, and (7+1) for black. This gives . Since we must select at least one ball, we subtract the one case where no balls are selected.
Final answer:
When selecting items from multiple groups where items within each group are identical (differing only in properties like color), we use the principle of combinations with repetition. For each group, we can choose any number from 0 to the total available. The total ways to select one or more balls is calculated by considering all possible selections from each group and subtracting the case where no balls are selected.
Step 1: Determine the number of choices for each color group. Since balls of the same color are identical, for white balls, we can choose 0, 1, 2, ..., up to 10. That gives 11 choices (including 0). Similarly, for green: 10 choices (0 to 9), and for black: 8 choices (0 to 7).
Step 2: The total number of ways to select balls (including selecting none) is the product of choices for each group:
Step 3: Subtract the case where no balls are selected (i.e., 0 white, 0 green, 0 black), which is 1 way.
Step 4: So, the number of ways to select one or more balls is:
Final Answer: 879
When selecting items from groups where the -th group has identical items, the number of ways to select any number of items (including none) is:
To find the number of ways to select one or more items, subtract 1 (the case of selecting none).