Answer
Verified
402.9k+ views
Hint: We will first start by finding the all ways of answering 5 questions by finding the way in which each question can be answered and then using the multiplication principle to find the total ways. Then we will subtract the case in which all answers are correct to find the final answer.
Complete step-by-step answer:
Now, we have been given a set of five questions with true or false answers. Also, it has been given that all the students have written different answers and no two students have given the same sequence of answers. Also, no student has written the correct answer.
Now, we know that each question has 2 options, therefore, 2 ways of answering a question. Similarly, each question out of five has 2 ways of answering. Now, from the fundamental principle of counting we have the total ways in which 5 questions can be answered as,
\[2\times 2\times 2\times 2\times 2=32\]
Now, in 32 ways there will be 1 way that gives all correct answers but it has been given that no one has given all the answers correctly. So, we have the total different ways of answering questions as $32-1=31$.
Now, since none of the students has the same sequence of answers, therefore, there can be at most 31 students in the class.
Note: To solve these types of questions it is important to note that we have used the fundamental principle of counting to find the total ways. Also, it is important to notice how we have first found the different sequence of answers possible and used it to find the number of students.
Complete step-by-step answer:
Now, we have been given a set of five questions with true or false answers. Also, it has been given that all the students have written different answers and no two students have given the same sequence of answers. Also, no student has written the correct answer.
Now, we know that each question has 2 options, therefore, 2 ways of answering a question. Similarly, each question out of five has 2 ways of answering. Now, from the fundamental principle of counting we have the total ways in which 5 questions can be answered as,
\[2\times 2\times 2\times 2\times 2=32\]
Now, in 32 ways there will be 1 way that gives all correct answers but it has been given that no one has given all the answers correctly. So, we have the total different ways of answering questions as $32-1=31$.
Now, since none of the students has the same sequence of answers, therefore, there can be at most 31 students in the class.
Note: To solve these types of questions it is important to note that we have used the fundamental principle of counting to find the total ways. Also, it is important to notice how we have first found the different sequence of answers possible and used it to find the number of students.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Using the following information to help you answer class 12 chemistry CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE