Question

a multiple-choice test contains 8 questions. there are four possible answers for each question. in how many ways can a student answer the questions on the test if the student answers every question?

Answer 1

There are the 105 ways with the help of combination by which the student answer the questions on the test.

According to the statement

we have to find the number of the ways can a student answer the questions on the test if the student answers every question.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

From the given information:

Test contains 8 questions and there are 4 possible answers.

Then we have to find the number of ways.

We use combination here which become

$C^{8} _{4}$

Now solve it then

$C^{8} _{4} = \frac{8!}{4! * 4!}$

$C^{8} _{4} = \frac{8*7*6*5*4!}{4! * 4!}$

$C^{8} _{4} = \frac{8*7*6*5}{ 4*3*2*1}$

$C^{8} _{4} = {7*3*5}$

Then multiply it and the answer become

105.

So, There are the 105 ways with the help of combination by which the student answer the questions on the test.

Learn more about combination here

brainly.com/question/11732255

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