Please show decision algorithm steps as best as possible. An example of a decision algorithm is as follows:

Step 1: ...

Alternative 1: ....

Alternative 2: ....

Step 2: ...

Alternative 1: ....

Alternative 2: ....

QUESTIONS:

1. The Delta Secret Philosophy society has just recruited three soccer players, two hockey players, and four Candy Crush players. The society president would like to select two of them to join the philosophical debate team, but must follow the strange rule that no two participants on the team can play the same type of game. How many choices does the president have? Must show decision algorithm by setting up alternatives/steps.

2. You are deciding on which stocks to include in your portfolio and your broker suggests three bond stocks, two mutual funds, and three index funds. She also advises you to choose two of each type.

a. Critique the following decision algorithm and calculation of the number of different collections of books you can take:

Step 1: Choose the first bond stock: 3 choices.

Step 2: Choose the second bond stock: 2 choices.

Step 3: Choose the first mutual fund: 2 choices.

Step 4: Choose the second mutual fund: 1 choice.

Step 5: Choose the first index fund: 3 choices.

Step 6: Choose the second index fund: 2 choices.

Hence, there are 322132 = 72 possible collections.

b. Supply a valid decision algorithm to calculate the correct number.

3. The following table shows fictitious share prices and yields of some extinct US companies:

Symbol	Company	Price ($)	Yield (%)
TWA	Trans World Airlines	27.23	3.62
PNAA	Pan American World Airways	38.30	0.12
EAL	Eastern Airline Inc	27.00	0.58
CPQ	Compaq Computers	6.92	0.35
GEFO	General Foods Corp	67.33	4
STOO	Standard Oil	72.58	0.14
RCA	Radio Corporation of America	60.47	0.61
STB	Studebaker Motor Company	27.18	2.17

You decide to make a small portfolio consisting of four of these companies selected at random.

a. How many possible portfolios of four stocks are possible in which all have yields of at least 0.3%?

b. How many possible five-stock portfolios are possible in which three of the stocks in your portfolio have the property that their price is more than $33 or their yield is below 0.3% (or both)?

c. How many possible five-stock portfolios are possible in which at least two of the stocks in your portfolio has a yield of more than 0.6%?