A test consists of 15 questions. Ten are true-false questions, and five are multiple-choice questions that have four choices each. A student must select an answer for each question. In how many ways can this be done?

Solution 7E

Step1 of 2:

We have a test it consists of total questions = 15.

True-False questions = 10 (that have 2 choices each)

Multiple choice questions = 5 (that have 4 choices each)

We need to find how many ways can this be done?

Step2 of 2:

The possible number of ways in True-False questions =

= 1024.

Hence, The possible number of ways in True-False questions is 1024.

Similarly,

The possible number of ways in Multiple choice questions =

= 1024.

Hence, The possible number of ways in Multiple choice questions is 1024.

Now,

The possible number of ways is given by

= (The possible number of ways in True-False questions)(The possible number of ways in

Multiple choice questions)

= 10241024

= 1048576.

Therefore, The possible number of ways is 1048576.

Conclusion:

Therefore, there are 1048576 ways are possible.