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? b) In how many ways can a student answer the questions on the test if the student can leave answers blank?

a) There are 4 possible answers for each question and we have 10 questions.

We can use the product rule: a student can answer the questions on the test in $4\times 4\times…\times 4=4^{10}$ ways.

b) In this case there are 5 possible answers for each question and we have 10 questions.

In this case we can also use the product rule: a student can answer the questions on the test in $5\times 5\times…\times 5=5^{10}$ ways.

Answers: a) $4^{10}$; b) $5^{10}$ .