We can use the multiplication principle. There are 10 ways to choose the president, 9 ways to choose the vice president, and 8 ways to choose the secretary. Therefore, the total number of ways is 10 x 9 x 8 = 720.

We can use the combination formula. The number of ways to choose 4 people out of 12 is given by C(12, 4) = 12! / (12 - 4)! / 4! = 495.

There are a total of 6 + 4 + 2 = 12 balls in the bag. The number of ways to choose 2 red balls out of 6 is C(6, 2) = 15. The number of ways to choose 1 blue ball out of 4 is C(4, 1) = 4. Therefore, the total number of ways to choose 2 red balls and 1 blue ball is 15 x 4 = 60. The probability of getting exactly 2 red balls and 1 blue ball is 60 / 12^3 = 1/15.

We can use the stars and bars method. We have 5 tasks and 3 employees, so we can represent the assignment as a string of 5 stars and 2 bars. For example, the string ||* represents the assignment of the first task to the first employee, the second and third tasks to the second employee, and the fourth and fifth tasks to the third employee. The number of different assignments is equal to the number of ways to arrange 5 stars and 2 bars, which is given by C(5 + 2, 2) = 243.

The salesman can visit the customers in any order, so we can use the permutation formula. The number of different orders is given by P(10, 10) = 10!.

We can use the combination formula. The number of ways to choose 10 applicants out of 20 is given by C(20, 10) = 20! / (20 - 10)! / 10! = 184756.

Each respondent can choose only one color, so the number of different ways to answer the question is equal to the number of colors, which is 5.

We can use the combination formula. The number of ways to choose 5 people out of 10 is given by C(10, 5) = 10! / (10 - 5)! / 5! = 252.

The probability of getting at least 1 red ball is equal to 1 minus the probability of getting no red balls. The probability of getting no red balls is given by (8/24)^4 = 1/256. Therefore, the probability of getting at least 1 red ball is 1 - 1/256 = 4/5.

We can first choose the president of the company, which can be done in 1 way. Then, we can choose the other 2 members of the committee from the remaining 11 employees, which can be done in C(11, 2) = 55 ways. Therefore, the total number of different committees is 1 x 55 = 220.

Each respondent can choose any number of sports from the list, so the number of different ways to answer the question is equal to 2^10 = 1024.

We can use the combination formula. The number of ways to choose 10 applicants out of 20 is given by C(20, 10) = 20! / (20 - 10)! / 10! = 184756.

There are a total of 10 + 8 + 6 = 24 balls in the bag. The number of ways to choose 2 red balls out of 10 is C(10, 2) = 45. The number of ways to choose 1 blue ball out of 8 is C(8, 1) = 8. The number of ways to choose 1 green ball out of 6 is C(6, 1) = 6. Therefore, the total number of ways to choose 2 red balls, 1 blue ball, and 1 green ball is 45 x 8 x 6 = 2160. The probability of getting exactly 2 red balls, 1 blue ball, and 1 green ball is 2160 / 24^4 = 1/20.

We can first choose the president of the company, which can be done in 1 way. Then, we can choose the other 3 members of the committee from the remaining 11 employees, which can be done in C(11, 3) = 165 ways. Therefore, the total number of different committees is 1 x 165 = 190.

Each respondent can choose any number of colors from the list, so the number of different ways to answer the question is equal to 2^5 - 1 = 31.