Questions: Evaluate the following expression. Express your answer as a fraction or a decimal number rounded to four decimal places. (n 1 C9) / (11 P4)

$Evaluate the following expression. Express your answer as a fraction or a decimal number rounded to four decimal places. (n 1 C9) / (11 P4)$

Transcript text: Evaluate the following expression. Express your answer as a fraction or a decimal number rounded to four decimal places. \[ \frac{{ }_{n 1} C_{9}}{{ }_{11} P_{4}} \]

Solution

Solution Steps

Step 1: Calculate the Combination

We need to evaluate the combination ${ }_{n} C_{9}$ where we assumed $n = 10$. The calculation gives us: \[ { }_{10} C_{9} = 10 \]

Step 2: Calculate the Permutation

Next, we calculate the permutation ${ }_{11} P_{4}$: \[ { }_{11} P_{4} = 7920 \]

Step 3: Evaluate the Expression

Now, we divide the result of the combination by the result of the permutation: \[ \frac{{ }_{10} C_{9}}{{ }_{11} P_{4}} = \frac{10}{7920} \approx 0.0012626262626262627 \]

Step 4: Round the Result

Finally, we round the result to four decimal places: \[ 0.0013 \]