A clothing company employs 36 workers on first shift and 19 workers on second shift. Five workers are chosen at random to be interviewed about the work environment. Find the probability of choose:

a) All first-shift workers
b) all second-shift workers
c) six first-shift workers
d) four second-shift workers

To find the probability, we need to consider the total number of workers and the number of workers we want to choose.

a) To find the probability of choosing all first-shift workers:
- Total number of workers = 36 + 19 = 55
- Number of ways to choose 5 workers from the first-shift workers = (36 choose 5)

So, the probability of choosing all first-shift workers is given by:
P(all first-shift workers) = (number of ways to choose 5 workers from the first-shift workers) / (total number of workers choose 5)

b) To find the probability of choosing all second-shift workers:
- Total number of workers = 55
- Number of ways to choose 5 workers from the second-shift workers = (19 choose 5)

So, the probability of choosing all second-shift workers is given by:
P(all second-shift workers) = (number of ways to choose 5 workers from the second-shift workers) / (total number of workers choose 5)

c) To find the probability of choosing six first-shift workers:
- Total number of workers = 55
- Number of ways to choose 6 workers from the first-shift workers = (36 choose 6)

So, the probability of choosing six first-shift workers is given by:
P(six first-shift workers) = (number of ways to choose 6 workers from the first-shift workers) / (total number of workers choose 5)

d) To find the probability of choosing four second-shift workers:
- Total number of workers = 55
- Number of ways to choose 4 workers from the second-shift workers = (19 choose 4)

So, the probability of choosing four second-shift workers is given by:
P(four second-shift workers) = (number of ways to choose 4 workers from the second-shift workers) / (total number of workers choose 5)

To calculate these probabilities, we need to use combinations (n choose r) which can be calculated using the formula:
n! / (r! * (n - r)!)

Now, you can substitute the appropriate values into the formulas to find the probabilities for each case.