Given the meaning and value of the symbol in the following
` ""^(5) P_2`

Answer

To solve the problem of finding the meaning and value of the symbol \( 5P2 \), we can follow these steps:

### Step 1: Understand the Meaning of the Symbol
The symbol \( nPr \) represents the number of permutations of \( n \) items taken \( r \) at a time. It indicates how many different ways we can arrange \( r \) items selected from a total of \( n \) items.

### Step 2: Write the Formula for Permutations
The formula for permutations is given by:
\[ nPr = \frac{n!}{(n - r)!} \]
where \( n! \) (n factorial) is the product of all positive integers up to \( n \).

### Step 3: Substitute the Values
In this case, we have \( n = 5 \) and \( r = 2 \). Therefore, we can substitute these values into the formula:
\[ 5P2 = \frac{5!}{(5 - 2)!} = \frac{5!}{3!} \]

### Step 4: Calculate the Factorials
Now, we need to calculate \( 5! \) and \( 3! \):
- \( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \)
- \( 3! = 3 \times 2 \times 1 = 6 \)

### Step 5: Substitute the Factorials into the Equation
Now we can substitute the values of the factorials back into the equation:
\[ 5P2 = \frac{120}{6} \]

### Step 6: Perform the Division
Now, we perform the division:
\[ 5P2 = 20 \]

### Conclusion
Thus, the value of \( 5P2 \) is \( 20 \).

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