Classify the following statements as 'true' or 'false' `:`
Number of ways of seating two person in two chairs out of n persons is `""^(n)P_(2)`

Answer

To determine whether the statement "Number of ways of seating two persons in two chairs out of n persons is \( nP_2 \)" is true or false, we can analyze the problem step by step.

### Step 1: Understand the Problem
We need to find the number of ways to seat 2 persons in 2 chairs from a total of \( n \) persons.

### Step 2: Identify the Formula
The formula for permutations, which is used when the order of selection matters, is given by:
\[ nP_r = \frac{n!}{(n-r)!} \]
where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.

### Step 3: Apply the Formula
In our case:
- \( n \) is the total number of persons.
- \( r \) is the number of chairs, which is 2.

Thus, we can substitute \( r = 2 \) into the permutation formula:
\[ nP_2 = \frac{n!}{(n-2)!} \]

### Step 4: Interpretation of the Result
The expression \( nP_2 \) gives us the number of ways to arrange 2 persons in 2 chairs from \( n \) persons. This is indeed the correct way to calculate the number of arrangements since the order in which the persons are seated matters (i.e., seating Person A in Chair 1 and Person B in Chair 2 is different from seating Person B in Chair 1 and Person A in Chair 2).

### Conclusion
Since the statement correctly describes the number of ways to seat 2 persons in 2 chairs out of \( n \) persons as \( nP_2 \), we classify the statement as **true**.

### Summary of Steps:
1. Understand the problem of seating 2 persons in 2 chairs.
2. Identify and apply the permutation formula \( nP_r \).
3. Substitute the values \( n \) and \( r = 2 \) into the formula.
4. Conclude that the statement is true based on the correct application of the formula.