Find the value of :
` ""^(5) C _2`

Answer

To solve the problem of finding the value of \( \binom{5}{2} \), we will use the formula for combinations.

### Step-by-Step Solution:

1. **Understand the Combination Formula**:
The formula for combinations is given by:
\[ \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
where \( n \) is the total number of items, \( r \) is the number of items to choose, and \( ! \) denotes factorial.

2. **Identify Values**:
In our case, \( n = 5 \) and \( r = 2 \).

3. **Substitute Values into the Formula**:
We substitute \( n \) and \( r \) into the combination formula:
\[ \binom{5}{2} = \frac{5!}{2!(5-2)!} \]

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

5. **Substitute Factorial Values**:
Now substitute these values back into the formula:
\[ \binom{5}{2} = \frac{120}{2 \times 6} \]

6. **Calculate the Denominator**:
Calculate the denominator:
\[ 2 \times 6 = 12 \]

7. **Final Calculation**:
Now perform the final division:
\[ \binom{5}{2} = \frac{120}{12} = 10 \]

### Final Answer:
Thus, the value of \( \binom{5}{2} \) is \( 10 \).

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