In an engineering entrance examination, there are only Multiple select questions (more than one option is correct). If a student selects any of the correct options, she will be awarded partial marks in proportion to the number of correct options she selects. If she chooses any of the wrong options, she will get zero marks for the entire question. In a particular question, there are four options of which the first three options are correct. In how many ways can the student get less than half of the marks allotted to the question assuming the student selects atleast one option?
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Answers
Answer:
11
Step-by-step explanation:
Case 1: 4 options= 1 way
Case 2: 3 options= 3 ways
Case 3: 2 options= 3 ways
Case 4: 1 option = 4 ways
total ways= 1+3+3+4=11
The number of ways = 11
Step-by-step explanation:
The student gets 0 marks if she choses any of the wrong answer
There are 3 correct options for the question
If each option carries 1 mark then the maximum marks that the student can get is 3
We have to find the ways in which the student gets either 0 or 1 mark (less than half of 3 i.e. 1.5 as she can't get 1.5 marks)
She will get zero marks if she selects the last option and any one of the three, any two of the three or all the three options
Thus, number of ways
= 1 × (³C₁ + ³C₂ + ³C₃)
= 3 + 3 + 1
= 7
She will get 1 marks if she selects any one of the three options that are correct
Therefore, number of ways
= ³C₁
= 3
Also if she selects only the 4th option then also she will get zero marks
She can select 4th option only in 1 way
Total number of ways in which she can get less than half of the marks allotted to the question
= 7 + 3 + 1
= 11 ways
Hope this answer is helpful.
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