Question

use the fundamental counting principle to determine the total number of outcomes.

1. picking a card from a standard deck then rolling a standard die.
2. choosing a random answer to the last five questions on a multiple-choice test if each question has four answer choices.
3. a mall has four escalators, one elevator, and three stairwells to travel from the second floor to the first floor. they have six doors on the first floor to exit the mall. if jane is on the second floor, how many ways can she exit the mall?

Explanation:

Problem 3

Step1: Determine card outcomes

A standard deck has 52 cards, so picking a card has 52 outcomes.

Step2: Determine die outcomes

A standard die has 6 faces, so rolling a die has 6 outcomes.

Step3: Apply Fundamental Counting Principle

Multiply the number of outcomes for each event: \( 52 \times 6 = 312 \).

Step1: Determine outcomes per question

Each multiple - choice question has 4 answer choices, so each question has 4 outcomes.

Step2: Determine total questions

There are 5 questions.

Step3: Apply Fundamental Counting Principle

Since for each of the 5 questions we have 4 choices, the total number of outcomes is \( 4^5=4\times4\times4\times4\times4 = 1024 \).

Step1: Determine travel options

The number of ways to travel from the second floor to the first floor: escalators (4) + elevator (1)+stairwells (3) = \( 4 + 1+3=8 \) ways.

Step2: Determine exit options

There are 6 doors to exit on the first floor.

Step3: Apply Fundamental Counting Principle

Multiply the number of travel options by the number of exit options: \( 8\times6 = 48 \).

Answer:

312

Problem 4