How many ways can 5 people be arranged in a straight line if there are 12 people to choose from
Number of choices for the first one=12
....
Number of choices for the fifth = 8
By the multiplication rule:
Number of ways = ....
12 * 8 = 60
12 * 8 = 96
Sorry, it's
12*11*10*9*8
=?
To find the number of ways to arrange 5 people in a straight line from a group of 12 people, we can use the concept of permutations.
In permutations, order matters, so we need to calculate the number of permutations for this scenario.
The formula to calculate permutations is given by:
P(n, r) = n! / (n - r)!
Where:
P(n, r) - Number of permutations of n distinct objects taken r at a time.
n - Total number of objects.
r - Number of objects taken at a time.
! - Factorial operator, which means multiplying all the positive integers from 1 to the given number.
In this case, we want to arrange 5 people from a group of 12, so we can calculate it as:
P(12, 5) = 12! / (12 - 5)!
= 12! / 7!
Now, let's calculate the factorial for each part:
12! = 12 * 11 * 10 * 9 * 8 * 7!
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1
Canceling out the common terms, we get:
P(12, 5) = 12 * 11 * 10 * 9 * 8
= 95,040
Therefore, there are 95,040 ways to arrange 5 people in a straight line from a group of 12 people.