Five socks, colored blue, brown, black, red, and purple, are in a drawer. How many combinations of three socks can be randomly selected from the drawer?
5! = 5 factorial = 5 * 4 * 3 * 2 * 1
n = total number of objects
r = number picked
nCr = n!/r!(n-r)!
To find the number of combinations of three socks that can be randomly selected from the drawer, we can use the concept of combinations or the binomial coefficient. The formula for the number of combinations, denoted as "nCk" or "C(n, k)", is:
C(n, k) = n! / (k! * (n - k)!)
Where "n" represents the total number of items or choices available, and "k" represents the number of items we want to select.
In this case, we have 5 socks and want to select 3 of them. So we can use the formula:
C(5, 3) = 5! / (3! * (5 - 3)!)
Simplifying the equation:
C(5, 3) = 5! / (3! * 2!)
= (5 * 4 * 3!) / (3! * 2 * 1)
= (5 * 4) / (2 * 1)
= 10
Therefore, there are 10 different combinations of three socks that can be randomly selected from the drawer.