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?
To find the number of combinations of three socks that can be randomly selected from the drawer, we can use the concept of combinations.
In this case, we have five socks, and we want to select three socks at a time.
The formula to calculate the number of combinations is:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items, and r is the number of items to be selected at a time.
Using this formula, we can calculate the number of combinations:
C(5, 3) = 5! / (3! * (5 - 3)!)
C(5, 3) = 5! / (3! * 2!)
C(5, 3) = (5 * 4 * 3!) / (3! * 2 * 1)
C(5, 3) = (5 * 4) / (2 * 1)
C(5, 3) = 10
Therefore, there are 10 different combinations of three socks that can be randomly selected from the drawer.
To find the number of combinations of three socks that can be randomly selected from a drawer containing five socks, you can use the formula for combinations.
The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items in the set
- r is the number of items chosen from the set
In this case, n = 5 (total number of socks) and r = 3 (number of socks chosen).
C(5, 3) = 5! / (3!(5-3)!)
Simplifying the equation:
5! = 5 x 4 x 3 x 2 x 1 = 120
3! = 3 x 2 x 1 = 6
(5-3)! = 2! = 2 x 1 = 2
C(5, 3) = 120 / (6 x 2)
C(5, 3) = 120 / 12
C(5, 3) = 10
So, there are 10 different combinations of three socks that can be randomly selected from the drawer.
To find all of the differennt ways to arrange r items out of n items. Use the combination formula below. (n stands for the total number of items; r stands for how many things you are choosing.)
nCr = n!/r!(n-r)!