Question

A multiple-choice test contains 10 questions. There are four possible answers for each question. a) In how many ways can a student answer the questions on the test if the student answers every question

Answer 1

`4^(10)` =1048576 ways a student can answer the questions on the test if the student answers every question.

Explanation:

Given that a multiple-choice test contains 10 questions and there are 4 possible answers for each question.

∴ Answers=4 options for each question.

To find how many ways a student can answer the given questions on the test if the student answers every question :

Solving this by product rule

Product rule :

If one event can occur in m ways and a second event occur in n ways, the number of ways of two events can occur in sequence is then m.n

From the given the event of choosing the answer of each question having 4 options is given by

The 1st event of picking the answer of the 1st question=4 ,

2nd event of picking the answer of the 2nd question=4 ,

3rd event of picking the answer of the 3rd question=4

,....,

10th event of picking the answer of the 10th question=4.

It can be written as by using the product rule

`=4.4.4.4.4.4.4.4.4.4`

`=4^(10)`

`=1048576`

∴ there are 1048576 ways a student can answer the questions on the test if the student answers every question.