What is the number of ways 9 people from a group of 13 could be arranged in a line.
To find the number of ways to arrange 9 people from a group of 13 in a line, we can use a concept called permutations.
In permutations, the order of the arrangement matters. We can use a formula to calculate the number of permutations:
P(n, r) = n! / (n - r)!
Where P(n, r) represents the number of permutations of n items taken r at a time, and the exclamation mark (!) denotes the factorial of a number.
In this case, we have 13 people in total, and we want to arrange 9 of them in a line, so we can calculate the permutation as follows:
P(13, 9) = 13! / (13 - 9)!
= 13! / 4!
To simplify this expression, we need to calculate the factorials of 13 and 4:
13! = 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
By canceling out common factors, we can simplify the expression further:
P(13, 9) = (13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1)
Calculating this expression will give us the number of ways to arrange 9 people from a group of 13 in a line.