If 7C4 is equal to 7C3, which of the following also holds true?

To understand why the correct answer is that 10C7 is equal to 10C3, we first need to explore the concept of combinations and the properties that govern them. The notation nCr represents the number of ways to choose r items from a set of n items without regard to the order of selection.

One of the key properties of combinations is that nCr equals nC(n-r). This means that the number of ways to choose r items from n is the same as the number of ways to choose (n - r) items from n.

In the case presented, we have 10C7. According to the property mentioned, this is equal to 10C(10-7), which simplifies to 10C3. Therefore, it holds true that 10C7 is equal to 10C3 because choosing 7 items also implies that you are leaving out 3 items, and both selections yield the same result.

This relationship helps in deducing the correct answer while also illustrating the underlying combinatorial reasoning. In summary, the equality of 10C7 and 10C3 is a direct application of the combination property, confirming that the correct option is indeed that they are equal.