Evaluate the expression ⁵C₂?

To evaluate the expression ⁵C₂, which represents the number of combinations of 5 items taken 2 at a time, we can use the combinations formula:

Combinations Formula

The formula for combinations is:

C(n, r) = n! / (r! * (n - r)!)

Where:

• n is the total number of items.
• r is the number of items to choose.
• ! denotes factorial, which is the product of all positive integers up to that number.

Applying the Formula

In this case, n = 5 and r = 2. Plugging these values into the formula gives:

C(5, 2) = 5! / (2! * (5 - 2)!)

Calculating Factorials

Now, we calculate the factorials:

• 5! = 5 × 4 × 3 × 2 × 1 = 120
• 2! = 2 × 1 = 2
• (5 - 2)! = 3! = 3 × 2 × 1 = 6

Putting It All Together

Substituting these values back into the formula:

C(5, 2) = 120 / (2 × 6) = 120 / 12 = 10

Final Result

Thus, the value of ⁵C₂ is 10.