Question

7.4
score: 5/17 answered: 5/17
question 6
evaluate.
c(6, 3) =
question help: ebook written example

Explanation:

Step1: Recall Combination Formula

The formula for combinations is \( C(n, k) = \frac{n!}{k!(n - k)!} \), where \( n! \) denotes the factorial of \( n \), defined as \( n! = n \times (n - 1) \times \dots \times 1 \) and \( 0! = 1 \). For \( C(6, 3) \), we have \( n = 6 \) and \( k = 3 \).

Step2: Calculate Factorials

First, compute the factorials:

• \( 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \)
• \( 3! = 3 \times 2 \times 1 = 6 \)
• \( (6 - 3)! = 3! = 6 \)

Step3: Substitute into Formula

Substitute these values into the combination formula:

$$ C(6, 3) = \frac{6!}{3!(6 - 3)!} = \frac{720}{6 \times 6} $$

Step4: Simplify the Expression

Simplify the denominator: \( 6 \times 6 = 36 \). Then divide: \( \frac{720}{36} = 20 \).

Answer:

20