Question

All six different robots have to be assigned to three different tasks. Three (3) robots have wheels only (Type I) and the other three (3) having legs only (Type II). Individual performance of the robots varies for a pending task due to the differences in failure rates, reliability and adaptability. Answer the following questions

: 1) If we plan to assign one (1) robot to Task 1, two (2) robots to Task 2, and three (3) to Task 3, in how many possible ways can the six robots be assigned to the three tasks?

2) If we assume that each task could be filled with nothing or up to 6 robots, in how many possible ways can the six robots be assigned to the three tasks?

3) If we assume that each task could be filled with nothing or up to 6 robots, what is the probability that exactly one (1) Type I robot is assigned to each task?

4) If we assume that each task could be filled with nothing or up to 6 robots, what is the probability that at least two (2) robots are assigned to Task 1 and that they belong to the same type?

Answer 1