Question

A quiz has eight multiple choice questions with four options for each ( A B C & D ) how many ways are there to answer the question

Answer 1

65,536 ways.

Explanation:

The Fundamental Counting Principle states that:

"If decision M can be made m ways and decision N can be made n ways, then the two decisions can be made m⋅n ways"

Therefore, we can create a model of the eight questions by drawing eight blanks:

_ _ _ _ _ _ _ _

Then, filling in each "question" with the number of options for each, which is four:

4 4 4 4 4 4 4 4

And finally, we can multiply the fours together, which would be 4⋅4⋅4⋅4⋅4⋅4⋅4⋅4 or 4⁸, which is equal to 65,536.

I hope this helps! :D

Answer 2

1680 ways.

Explanation:

This question is solved using Permutation formula.

Permutation formula is given as

nPr = n! / (n -r)!

In the above question we are to find how many ways we can answer 8 multiple choice questions with 4 options(A, B,C,D)

Therefore,

n = 8 multiple choice questions

r = 4 options

nPr = n! / (n - r)!

8P4 = 8! / ( 8 - 4) !

8P4 = 8! / 4!

8P4 = (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (4 × 3 × 2 × 1)

8P4 = 40320 / 24

8P4 = 1680 ways

Therefore, the number of ways to answer 8 multiple choice questions with 4 options (A, B, C, D) for each is 1680 ways.