To find out how many combinations can be formed by selecting 2 items from a total of 5 items, we can use the combinations formula. The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where:
– n = total number of items (in this case, 5)
– r = number of items to choose (in this case, 2)
– ! = factorial, which is the product of an integer and all the integers below it.
Using the formula:
C(5, 2) = 5! / (2!(5-2)!) = 5! / (2! * 3!)
Calculating the factorials:
- 5! = 5 x 4 x 3 x 2 x 1 = 120
- 2! = 2 x 1 = 2
- 3! = 3 x 2 x 1 = 6
Now substituting back into the formula:
C(5, 2) = 120 / (2 * 6) = 120 / 12 = 10
So, there are a total of 10 combinations of selecting 2 items from 5 items.