To find the number of different professional committees of 8 people that can be formed, each containing at least 2 Doctors, at least 2 Public Servants, and 1 IT Expert from a list of 7 Doctors, 6 Public Servants, and 6 IT Experts, we can use combinations.
Let's break down the conditions:
1. At least 2 Doctors: This means we can choose 2, 3, 4, 5, 6, or 7 Doctors.
2. At least 2 Public Servants: This means we can choose 2, 3, 4, 5, or 6 Public Servants.
3. Exactly 1 IT Expert: This means we choose 1 IT Expert.
Now, we can find the total number of ways to form the committee by multiplying the number of ways to choose from each category:
\[ \text{Total number of committees} = (\text{Ways to choose Doctors}) \times (\text{Ways to choose Public Servants}) \times (\text{Ways to choose IT Experts}) \]
Let's calculate:
\[ \text{Ways to choose Doctors} = C(7, 2) + C(7, 3) + C(7, 4) + C(7, 5) + C(7, 6) + C(7, 7) \]
\[ \text{Ways to choose Public Servants} = C(6, 2) + C(6, 3) + C(6, 4) + C(6, 5) + C(6, 6) \]
\[ \text{Ways to choose IT Experts} = C(6, 1) \]
Now, calculate the combinations and find the product to get the total number of committees.
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