In how many ways can a committee of 4 be selected out of 12 persons so that a particular person may
never be taken?

Answer

To solve the problem of selecting a committee of 4 from 12 persons such that a particular person is never included, we can follow these steps:

### Step 1: Identify the total number of persons
We start with a total of 12 persons.

### Step 2: Exclude the particular person
Since we want to ensure that a particular person (let's call them Person A) is never included in the committee, we exclude Person A from our selection. This leaves us with 11 persons to choose from.

### Step 3: Determine the committee size
We need to form a committee of 4 members. Since we have excluded Person A, we will select all 4 members from the remaining 11 persons.

### Step 4: Calculate the number of combinations
The number of ways to choose 4 persons from the remaining 11 can be calculated using the combination formula:
\[ \text{Number of ways} = \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
where \( n \) is the total number of persons to choose from (11 in this case), and \( r \) is the number of persons to choose (4).

Thus, we calculate:
\[ \binom{11}{4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4! \cdot 7!} \]
This simplifies to:
\[ \binom{11}{4} = \frac{11 \times 10 \times 9 \times 8}{4 \times 3 \times 2 \times 1} = \frac{7920}{24} = 330 \]

### Final Answer
Therefore, the number of ways to select a committee of 4 persons from 12 persons, ensuring that a particular person is never included, is **330**.

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