Math Problem Statement

Evaluate \(9C_4\)

Solution

The problem presented is to evaluate (94)\binom{9}{4}, which represents the number of ways to choose 4 objects from a set of 9, also known as a combination.

The formula for combinations is:

(nr)=n!r!(nr)!\binom{n}{r} = \frac{n!}{r!(n-r)!}

In this case, n=9n = 9 and r=4r = 4, so the calculation is:

(94)=9!4!(94)!=9!4!5!\binom{9}{4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!}

Let me calculate it for you.The value of (94)\binom{9}{4} is 126126. Therefore, the correct answer is the third option: 126.

Would you like further details or have any other questions?

Here are five related questions:

  1. How would you calculate (103)\binom{10}{3}?
  2. What is the difference between combinations and permutations?
  3. How would the formula change if you were calculating permutations instead of combinations?
  4. What is (95)\binom{9}{5}, and how is it related to (94)\binom{9}{4}?
  5. What does the factorial symbol (!) represent in mathematics?

Tip: The combination formula is symmetric, meaning (nr)=(nnr)\binom{n}{r} = \binom{n}{n-r}.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Factorials

Formulas

\(\binom{n}{r} = \frac{n!}{r!(n-r)!}\)

Theorems

Combination formula

Suitable Grade Level

Grades 8-10