Kenneth Rosen- Counting-3.a,b

Question

A multiple choice test contains $10$ questions There are $4$ possible answers for each question?

$a)$How many ways can a student answer the questions on the test if the student answers every question?

$b)$How many ways can a student answer the questions on the test if the student can leave answers blank?

Answer 1

a)

If the student has to answer every question without leaving any question blank,

then there are $4$ options and the student can select any one out of these $4$ options in each question

So the number of ways he can answer each question =$4$ ways

$\therefore$ Number of ways to answer $10$ questions$=4*4*4.......(10 $ times$)$

Ans= $4^{10}$ ways

---

b)

If a student can leave an answer blank,

then the student can either select any one out of the $4$ options or leave it blank for each question

So the number of ways he can answer each question=$5$ ways

$\therefore$ Number of ways to answer $10$ questions$=5*5*5......(10 $ times$)$

Ans=$5^{10}$ ways

Comments

thanks  bhagyashree