how many ways can one arrange k people in a row
To find the number of ways to arrange k people in a row, you can use the concept of permutations.
The formula for permutations is P(n, r) = n! / (n - r)!.
In this case, n represents the number of available people (which is assumed to be greater than or equal to k), and r represents the number of people to be arranged (which is k in this case).
So, to find the number of ways to arrange k people in a row, you need to calculate P(n, k).
Let's take an example:
Suppose you have 5 people (n = 5) and you want to arrange 3 of them (k = 3) in a row.
Using the formula, you can calculate the number of ways as follows:
P(5, 3) = 5! / (5 - 3)!
= 5! / 2!
= (5 × 4 × 3 × 2 × 1) / (2 × 1)
= (120) / (2)
= 60
Therefore, there are 60 ways to arrange 3 people out of 5 in a row.