Question

For a research study, there are five options for the first question, four options for the second question, and three options for the third question. Using a list, there would be (blank1) outcomes for the sample space. For a similar study, if there are only four options for the first question, the sample space would have (blank2) outcomes.

B1 (140) (60) (20)
B2 (16) (24) (48)

Answer 1

`\large\boxed{blank 1\text{ }(60)}\\ \\ \large\boxed{blank 2\text{ }(48)}`

Step-by-step explanation:

To find how many outcomes there would be for the sample space, you need to use the fundamental principle of counting, which simply states that if there are m possible outcomes for one event and n possible outcomes for other event, then there are m × n outcomes for both joint events.

Thus, for the research study where there are five options for the first question, four options for the second question, and three options for the third question, the sample space is constituted by 5 × 4 × 3 = 60 outcomes.

For the similar study, if there are only four options for the first question, the sample space would have 4 × 4 × 3 = 48 outcomes.