A trader is designing his investment portfolio. He has prepared a list of potential companies in which to  purchase stock. These include 5 companies in agriculture, 6 companies in manufacturing and 9  companies in the high-tech industry. The trader is going to print this list of companies. a) In how many different orders can he print the list?
b) If we just look at the categories of the companies, how many different orders are there in which to  print the list?
c) The trader will select 5 stocks from the list in which he will invest. How many ways can he select these?
d) What is the probability that he will pick at least 2 high-tech stocks?
e) What's the probability that the trader's pick-five contains 2 in agriculture, 1 in heavy industry and 2 in  high-tech industry?
f) If the trader plans to invest in at least one stock from the full list of 20, how many different  investment plans can he design