Aaron is designing a party game in which he needs exactly 24 possible outcomes. Which sets of actions can he use to have a statistically fair game?

Counting from the top:

fist option

fourth option

fifth option.

Step-by-step explanation:

Any set that has a multiplicative outcome, such that the total number of outcomes is 24.

Remember that if we have a combination of two events, one with N outcomes and the other with M outcomes, the total number of outcomes is:

M*N

This is the main thing we need to see.

Let's analyze each option:

1) flip a coin (2 outcomes)

  flip a coin again (2 outcomes)

  roll a 6 sided dice ( 6 outcomes)

total number of outcomes:

2*2*6 = 24

2) Selecting a number from 1 to 16 (16 outcomes) and rolling a dice of 8 sides (8 outcomes).

The total number of outcomes is:

8*16 = 128

We wanted only 24.

3) Selecting a number from the set {1, 3, 5, 7, 9} (5 outcomes)

   flip a coin (2 outcomes)

   flip the coin again (2 outcomes)

total number of outcomes:

2*2*5 = 20

We wanted 24, we can discard this.

4) Spin the thing (3 outcomes)

   roll an 8-sided dice (8 outcomes)

Total number of outcomes:

8*3 = 24

This is a correct option.

5) Select a card from A to D (4 outcomes)

Roll the thing (6 outcomes)

total number of outcomes:

6*4 = 24

This is a correct option.

6) Select a card from A to N {14 options}

   Roll the thing once (10 outcomes)

Total number of outcomes:

14*10 = 140

We wanted 24, so we can discard this option.

Then the correct options are:

first one, fourth one, and fifth one.

ok

step-by-step explanation: