Question

On a math test there are 10 multiple-choice questions with 4 possible answers and 15 truefalse questions. In how many possible ways can the 25 questions be answered?

Answer 1

There are 10 multiple question with 4 possible answers. Hence there 4 options for each question therefore there is

4*4*...*4 (10 times) = 4^10 ways to answer. (In case if one answer is correct ).

If there are multiple answers to the each question and we have atleast one answer to each question then we have 4C1 + 4C2 + 4C3 + 4C4 = 15 ways then we have 15^10 ways

There are 15 true false question so there are 2^15 possible way to answer .  

Since both events are independent therefore total number of possible ways is 4^10 + 2^15.

In case of multiple answer to question we have 15^10 + 2^15 ways