The expression \( 4C4 \) represents a combination, which calculates how many ways you can choose 4 objects from a set of 4. The formula for combinations is:

\[
nCk = \frac{n!}{k!(n-k)!}
\]

In this case, \( n = 4 \) and \( k = 4 \), so:

\[
4C4 = \frac{4!}{4!(4-4)!} = \frac{4!}{4! \cdot 0!}
\]

Since \( 0! = 1 \), we have:

\[
4C4 = \frac{4!}{4! \cdot 1} = \frac{4!}{4!} = 1
\]

So, \( 4C4 = 1 \).

Would you like more details or have any questions about combinations? 

Here are some related questions:
1. What is the formula for permutations, and how does it differ from combinations?
2. How do you calculate \( 5C3 \)?
3. What is the value of \( 6C2 \)?
4. Can you explain the difference between combinations and arrangements?
5. How can combinations be used in probability problems?

**Tip:** Combinations are used when the order of selection doesn't matter, while permutations are used when the order does matter.

Learn how to evaluate the combination 4C4 using the combination formula nCk = n! / (k!(n-k)!). This detailed guide explains how 4C4 equals 1 by applying the factorial formula and understanding key combinatorial concepts. Suitable for Grades 9-12 students studying combinatorics.

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