A multiple choice test consists of 10 questions, each question with five possible answers but only one correct answer. In how many different ways can a student check off one answer to each questions? In how many different ways can a student check off one answer to each question and get all the answer wrong?

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In how many different ways can a student check off one answer to each questions?

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each question with five possible answers but only one correct answer.

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You really cannot answer this one?

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In how many different ways can a student check off one answer to each question and get all the answer wrong?

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Find how many ways the student gets an answer wrong, and multiply each time by the number of ways of getting the next answer wrong.

e.g.
If there are 10 ways of getting the first and second answers wrong, then there are 100 ways of getting both answers wrong.

If there are 2 ways of getting each of 5 answers wrong each, there there are 2*2*2*2*2 = 128 ways of getting all 5 answers wrong.