Question

On a multiple choice test with 100 questions and 5 answer per question, how many different ways can the test be completed? (b) On a multiple choice test with 10 equations and 5 answers per question, how many different ways can the test be completed if no two consecutive answers are ever the same?

Answer 1

Answer and Step-by-step explanation:

(a)

Given that a multiple choice test consist of 100 questions such that there are 5 answers per question i.e., any of the 5 answers can be selected i.e., there are 5 ways of selecting an answer

Total no. of ways of completing the test =$5^{100}$  ways

(b)

In order to complete the test in a way that 2 consecutive answers should never be the same, question can be answered such that  only one of the 5 option is selected.

Therefore, answer to the first question can be given in 5 ways

to the next in 4 ways and for all other only 4 ways are there to answer the question for 10 equations.

So,

Total no. of ways to answer the given question =

$5\times 4\times 4\times 4\times 4\times 4\times 4\times 4\times 4\times 4 = 1310720$ ways