# (a) How many different professionals committees of 8 people can be formed, each containing at least 2 Doctors, at least 2 Public Servants and 1 IT Expert from list of 7 Doctors, 6 Public Servants and 6 IT Experts?

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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.