The value of ⁶C₄ is-

• A) 6
• B) 9
• C) 15
• D) 240

To find the value of ⁶C₄, which represents the number of combinations of 6 items taken 4 at a time, we can use the formula for combinations:

Combination 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.

Calculating ⁶C₄

In this case, n = 6 and r = 4. Plugging these values into the formula gives:

C(6, 4) = 6! / (4! * (6 - 4)!)

This simplifies to:

C(6, 4) = 6! / (4! * 2!)

Factorial Values

Now, we calculate the factorials:

• 6! = 720
• 4! = 24
• 2! = 2

Putting It All Together

Now substituting back into the equation:

C(6, 4) = 720 / (24 * 2) = 720 / 48 = 15

Final Answer

Thus, the value of ⁶C₄ is 15. The correct option is C) 15.