Periorm the indicated calculation. $$ { }_{6} P_{4} $$

Question

UpStudy AI · Accepted Answer

Below are the step-by-step details for calculating $$ _{6}P_{4} $$ using the permutation formula.

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### Step 1: Recall the Permutation Formula

For permutations, the formula for choosing and ordering $$ k $$ items from a total of $$ n $$ items is:

$$
_{n}P_{k} = \frac{n!}{(n-k)!}
$$

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### Step 2: Substitute the Values

In this problem, $$ n = 6 $$ and $$ k = 4 $$. Substitute these into the formula:

$$
_{6}P_{4} = \frac{6!}{(6-4)!} = \frac{6!}{2!}
$$

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### Step 3: Compute the Factorials

- Compute $$ 6! $$ (6 factorial):

$$
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720
$$

- Compute $$ 2! $$ (2 factorial):

$$
2! = 2 \times 1 = 2
$$

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### Step 4: Perform the Division

Now, divide $$ 6! $$ by $$ 2! $$:

$$
\frac{6!}{2!} = \frac{720}{2} = 360
$$

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### Final Answer

$$
_{6}P_{4} = 360
$$
$$_{6}P_{4} = 360$$

Periorm the indicated calculation. \( { }_{6} P_{4} \)