Using r code, solve the following questions:

1. Dr. Nuttelman has 12 students in one of his classes. How many arrangements of 3 students can be put together if order matters? Store your final answer in the variable PartA.

2. A manufacturing company produces metal bushings. One out of every 10 (10%) of the bushings do not conform to specifications. What is the probability that, of 10 bushings produced, at least 6 of them are to specification? Store your final answer in the variable PartC.

3. A manufacturing company produces metal bushings. One out of every 10 (10%) of the bushings do not conform to specifications. If the company needs to produce 10 bushings that meet specifications, what is the probability that the 10th success will occur by the 12th bushing that is manufactured? Store your final answer in the variable PartD.

4. Male human height in the Netherlands is a normally distributed variable with mean 6 feet (72 inches) and standard deviation 4 inches. A third (1/3) of men in the Netherlands will have a height of greater than what value, in inches? Store your final answer in the variable PartG.