A permutation is an arrangement of objects without repetition where order matters. A 3-permutation of a set s is an arrangement of 3 elements from s in a particular order.
Given a set s of 5 elements, {1, 2, 3, 4, 5}, we're asked to find the number of 3-permutations.
We use the formula for permutations which is: P(n, r) = n! / (n-r)!
Here, n is the total number of elements in the set s, which is 5.
Thus, n=5.
And r represents the length of the permutation or the number of terms in the arrangement, which in this case is 3.
So, r=3.
In this case, we will plug in n=5, and r=3 in the formula for permutations P(n, r) = n! / (n-r)!
This gives us: P(5,3) = 5! / (5-3)!
Calculating the factorial values, we have 5! = 5×4×3×2×1 = 120,
and (5-3)! = 2! = 2×1 = 2.
We then divide 120 by 2, yielding a result of 60.
So, the number of 3-permutations of the set s={1, 2, 3, 4, 5} is 60.