Final answer:
The number of distinct ordered triples (x, y, z) from a set of natural numbers from 1 to 6 is 120, calculated by multiplying the number of choices for each element in the triple consecutively (6*5*4).
Step-by-step explanation:
The question seems to be asking for the number of ordered triples (x, y, z) from a set a of natural numbers from 1 to 6, where all elements are distinct. Since the set contains exactly 6 natural numbers, the total number of ways to pick x is 6 (since it could be any of the numbers). After picking an x, there are 5 choices left for y, and then only 4 choices left for z, as we are not allowed to repeat numbers.
Therefore, the total number of ordered triples (x, y, z) is 6 * 5 * 4, since we are performing permutations of 6 items taken 3 at a time without replacement. When we calculate this, we get 120 possible ordered triples.