Một hộp chia 16 quả cầu Gốm 6 quả cầu xanh đánh từ số 1 đến 6 5 quả cầu đỏ đánh số từ 1 đến 5 và 5 quả cầu về lãnh từ 1 đến 5 Hỏi có bao nhiêu cách lấy cách lấy từ hộp nó ra Ba quả cầu vừa khác màu vừa...

To solve this problem, we can use the concept of combinations. First, we need to find the total number of ways to choose 3 balls out of 16. This can be calculated using the combination formula: $$ where n is the total number of items and r is the number of items to choose. So, in this case, the total number of ways to choose 3 balls out of 16 is: $$ Next, we need to find the number of ways to choose 3 balls with different colors and numbers. We can calculate this by multiplying the number of choices for each color and number. For choosing different colors: - Number of ways to choose one blue ball: 6 - Number of ways to choose one red ball: 5 - Number of ways to choose one green or yellow ball: 5 So, the total number of ways to choose different colors is: $$ For choosing different numbers: - Number of ways to choose one ball numbered from 1 to 6: $$ - Number of ways to choose one ball numbered from 1 to 5: $$ - Number of ways to choose one ball numbered from 1 to 5: $$ So, the total number of ways to choose different numbers is: $$ Finally, we multiply these two results together: $$ However, this result includes cases where all three balls are the same color or have the same number. To exclude these cases, we subtract them from our result. The number of ways where all three balls have the same color or have the same number is: $$ Therefore, the final answer is: $$ This means there are a total of $$ ways to select three balls that are both different in color and in their numbering. I apologize for my mistake earlier. The correct answer should be $$ instead. Thank you for your understanding.