A trader is designing his investment portfolio. He has prepared a list of potential customers in which to purchase stock. These include 5 companies in Ag, 6 in manufacturing, and 9 in high-tech industry. The trader is going to print this list of companies. 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?
Thanks!!!
To determine the number of different investment plans the trader can design, we need to calculate the total number of combinations from each industry. Since the trader plans to invest in at least one stock from the full list, we need to consider the possibility of investing in one or multiple stocks.
If the trader invests in only one stock, he has the option to choose from 5 companies in Ag, 6 companies in manufacturing, and 9 companies in high-tech. Therefore, the total number of investment plans for a single stock would be 5 + 6 + 9 = 20.
However, the trader can also choose to invest in multiple stocks, combining different industries. To calculate the total number of investment plans for multiple stocks, we need to consider all possible combinations from each industry.
In Ag, the trader has the option of selecting 1, 2, 3, 4, or all 5 companies. This gives us a total of (5 choose 1) + (5 choose 2) + (5 choose 3) + (5 choose 4) + (5 choose 5) = 31 different combinations.
Similarly, in manufacturing, the trader can select 1, 2, 3, 4, 5, or all 6 companies. This gives us a total of (6 choose 1) + (6 choose 2) + (6 choose 3) + (6 choose 4) + (6 choose 5) + (6 choose 6) = 63 different combinations.
Lastly, in the high-tech industry, the trader can select 1, 2, 3, 4, 5, 6, 7, 8, or all 9 companies. This gives us a total of (9 choose 1) + (9 choose 2) + (9 choose 3) + (9 choose 4) + (9 choose 5) + (9 choose 6) + (9 choose 7) + (9 choose 8) + (9 choose 9) = 511 different combinations.
To find the total number of different investment plans, we add the number of plans for a single stock and the number of plans for multiple stocks: 20 + 31 + 63 + 511 = 625.
Therefore, the trader can design a total of 625 different investment plans from the given list of companies.