Question

Find the total of number of ways of answering $4$ multiple choice questions, each having $4$ choices?

• A. $4\times 4\times 4\times 4$
• B. $256$
• C. $(4{)}^4$
• D. $128$

Answer 1

Answer: (A), (B), (C)

$(4{)}^4$

Given, there are $4$ MCQ type questions each having four choices.

First question can be answered in $4$ different ways.

Second question can be answered in $4$ different ways.

Third question can be answered in $4$ different ways.

And, fourth question can also be answered in $4$ different ways.

This is similar to filling of $4$ vacant places having $4$ options of filling with repetition as shown:


Since we have to choose number of ways of answering first and second and third and fourth question.(AND means multiplication by counting principle).

So, total number of ways for answering $4$ questions are $4\times 4\times 4\times 4=(4{)}^4=256.$