A multiplechoice test contains 10 questions There are four p

A multiple-choice test contains 10 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? In how many ways can a student answer the questions on the test if the student can leave answers blank?

Solution

Ans(a):

since each question has 4 choices so

first question can be answered in 4 ways

second question can be answered in 4 ways

similarly each of 10 questions can be answered in 4 ways

so total number of ways = 4x4x4x4x4x4x4x4x4x4=4^10=1048576

so final answer is 1048576

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Ans(b):

student can leave answer blank means now student has 5 choice for each question

so process will be same and answer becomes 5^10 which is 9765625