To find the number of ways to choose one person for each of the four different positions from 70 applicants, we can use the concept of permutations.
The number of ways to choose the designer from 70 applicants is 70.
The number of ways to choose the engineer from the remaining applicants is 69.
The number of ways to choose the manager from the remaining applicants is 68.
The number of ways to choose the secretary from the remaining applicants is 67.
Therefore, the total number of ways to choose one person for each of the four different positions is:
70\times69\times68\times67=22005480
\boxed{22005480} ways to choose one person for each of the four different positions from 70 applicants.