To find the value of 7C4, we need to understand that 7C4 represents the number of combinations of 7 items taken 4 at a time. This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n – r)!)
In our case, n is 7 and r is 4. Plugging these values into the formula, we have:
C(7, 4) = 7! / (4! * (7 – 4)!)
Calculating each factorial:
- 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
- 4! = 4 × 3 × 2 × 1 = 24
- (7 – 4)! = 3! = 3 × 2 × 1 = 6
Now, substituting back into the equation gives us:
C(7, 4) = 5040 / (24 * 6)
This simplifies to:
C(7, 4) = 5040 / 144 = 35
Therefore, there are 35 different ways to choose 4 items from a set of 7. In summary, 7C4 equals 35, which represents the number of unique combinations of 4 items from 7.