There are 20 variations of 5 elements taken 2 at a time without repetition.
What is permutation?
Permutation is the arrangement of objects in a specific order. It represents the number of ways elements can be ordered.
Let's calculate using the formula for permutations:
P(n, r) = n!/(n-r)!
n = 5 = number of elements
r = 2 = taken two at a time
Substituting these values:
P(5, 2) = 5!/(5-2)!
P(5, 2) = 5!/3!
P(5, 2) = 5 * 4 * 3!/3!
P(5, 2) = 5* 4/1
P(5, 2) = 20
So, there are 20 variations of 5 elements taken 2 at a time without repetition.