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  • A multiple choice question test with all the questions mandatory to be answered can be attempted in 2047 ways such that the student gets at least one question right. Find the number of wa

A multiple choice question test with all the questions mandatory to be answered can be attempted in 2047 ways such that the student gets at least one question right. Find the number of ways in which he can answer 4 questions correctly.

 

Option: 1
330

 


Option: 2

230


Option: 3

420

 


Option: 4

320


Answers (1)

best_answer

Given that,

Any question can be answered in one of two ways (correct or incorrect). 

Let N be the number of questions.

\begin{aligned} & 2^n-1=2047 \\ & 2^n=2048 \\ & 2^n=2^{11} \end{aligned}

Thus,

n=11

The number of ways in answering 4 answers correctly is,

{ }^{11} C_4=\frac{11 !}{4 ! 7 !}\\

{ }^{11} C_4=330

Therefore, the number of ways is 330 ways.

Posted by

avinash.dongre

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