Question

There are 10 true-false questions. The number of ways in which they can be answered is
(A). 10!
(B). $2^{10}$
(C). 10
(D). $10^{2}$

Answer 1

Hint: In this question it is given that there are 10 true-false questions, then we have to find the number of ways in which the questions can be answered. So to find the solution we need to know that if there are n number of options there then one can select one option in n number of different ways.

Complete step-by-step solution:
Here it is given that 10 questions are there and each question has two options either it is true or false.
So a student can answer one question in 2 different ways.
Therefore for each of the questions the student will get two options.
Now since all the questions are independent to each other so the total number of ways to answer 10 questions can be found by multiplying the number of ways to answer each question.
So number of ways to answer all the 10 question will be
=$2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$
=$2^{10}$
Therefore, we can say that a student can answer 10 true-false questions in $2^{10}$ different ways.
Hence the correct option is option B.

Note: While finding the solution you need to know that if two events are independent then the outcome of one event is not affected by another event.
Also we have applied the fundamental principle of multiplication, so in combinatorics, the rule of product or multiplication principle is a basic counting principle which states that if there are A ways of doing something and B ways of doing another thing, then there are $A\times B$ ways of performing both actions.