Question

you are taking a​ multiple-choice test that has 7 questions. Each of the questions has 4 answer​ choices, with one correct answer per question. If you select one of these choices for each question and leave nothing​ blank, in how many ways can you answer the​ questions?

Answer 1

The total number of ways we can answer the questions is 78125.

Explanation:

Given : You are taking a​ multiple-choice test that has 7 questions. Each of the questions has 4 answer​ choices, with one correct answer per question. If you select one of these choices for each question and leave nothing​ blank.

To find : How many ways can you answer the​ questions?

Solution :

Each question has 4 answer choices.

If you select one of these choices for each question and leave nothing​ blank.

i.e. For 1 question number of ways to attempt 1st question is 4 ways

For 2 question number of ways to attempt 2nd question is 4 ways

Similarly, for 7th question number of ways to attempt 7th question is 4 ways.

So, Number of ways we can answer the questions is
`5* 5* ..5`

`\text{Number of ways}=5^7`

`\text{Number of ways}=78125`

Therefore, The total number of ways we can answer the questions is 78125.