The expression you provided is:

\[
\frac{38!}{(38-21)!21!} = \frac{38!}{17! \cdot 21!}
\]

This is a combination formula, often written as:

\[
C(38, 21) = \frac{38!}{(38-21)!21!} = \frac{38!}{17!21!}
\]

Now, let's solve for \(C(38, 21)\).

First, we use the formula:

\[
C(n, r) = \frac{n!}{(n-r)!r!}
\]

Thus,

\[
C(38, 21) = \frac{38 \times 37 \times \cdots \times 18}{21!}
\]

Let me calculate the result for you.The value of \( \frac{38!}{17! \cdot 21!} \) or \( C(38, 21) \) is \( 28,781,143,380 \).

Would you like further details or have any questions?

Here are five related questions for further exploration:
1. How is the combination formula derived?
2. What is the difference between combinations and permutations?
3. How would the answer change if the numbers were \( C(38, 20) \)?
4. Can you calculate the value of \( C(40, 22) \)?
5. How do combinations apply in probability theory?

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

Learn how to solve the combination problem 38!/(38-21)!21!, which involves factorials and the combination formula. Understand how C(38, 21) is computed step-by-step, using combinatorics and algebraic concepts. This problem is suitable for students in Grades 9-12 and covers key ideas like factorial simplification.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation