how many ways can you line up 11 people for a picture?
To find the number of ways to line up 11 people for a picture, you can use the concept of permutation because the order in which people are arranged matters.
The formula for permutation is:
P(n, r) = n! / (n - r)!
Where:
- P(n, r) represents the permutation of "n" objects taken "r" at a time
- n! denotes the factorial of "n" (the product of all positive integers less than or equal to "n").
In this case, we have 11 people (n = 11) and we want to arrange all of them (r = 11). Plugging these values into the formula, we get:
P(11, 11) = 11! / (11 - 11)!
= 11! / 0!
= 11!
Since 0! is defined as 1, we can simplify further:
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 39,916,800
Therefore, there are 39,916,800 different ways to line up 11 people for a picture.