Question

Compute the following

n! / (n-k-1)!

Answer 1

(n-k-1)! = 1*2*3*...*(n-k-1)

so when you divide n! by that you get
n(n-1)...(n-k)

read up on falling factorials

Answer 2

n! = n(n-1)(n-2)...3*2*1

(n-k-1)! = (n-k-1)(n-k-2)(n-k-3)...*3*2*1

Thus, n!/(n-k-1)! = n(n-1)...(n-k)

Answer 3

[AI-generated answer — Explain Bot]

To compute the expression n! / (n-k-1)!, you will need to understand the concept of factorials and how to calculate them.

Factorial (!) represents the product of all positive integers from 1 to the given number. For example, 5! (read as "5 factorial") can be calculated as: 5! = 5 x 4 x 3 x 2 x 1 = 120.

Now let's break down the expression step by step:

1. Determine the value of n. This represents the number for which you want to calculate the factorial.

2. Calculate the factorial of n, denoted as n!, by multiplying all the positive integers up to n. For example, if n = 5, then 5! = 5 x 4 x 3 x 2 x 1.

3. Determine the value of k. This represents the number that will be subtracted from n in the next step. Make sure k is less than or equal to n.

4. Subtract (k + 1) from n. For example, if n = 5 and k = 2, then (n - k - 1) = (5 - 2 - 1) = 2.

5. Calculate the factorial of (n - k - 1), denoted as (n - k - 1)!. In the previous example, (2)! = 2 x 1 = 2.

6. Divide n! by (n - k - 1)!. Continuing with the example, n! / (n - k - 1)! = 5! / (2)! = 120 / 2 = 60.

Therefore, for any given value of n and k, you can compute the expression n! / (n - k - 1)! using these steps.