Finding no. of combinations for the situation

  • #1

Homework Statement


Refer the image

Homework Equations


Equations for permutations and combinations

The Attempt at a Solution


Let x be the no. of questions that turned out to be correct. So total score will be 3x-(10-x)=4x-10.
The value of this expression must be from the given set and since x is an integer, the only no. satisfying the condition from the set is 18. (4(7)-10=18).
Hence 7 questions were correct and 3 incorrect. So, no. of ways of choosing 7 questions from 10 would be 10C7 = 120. Isn't this what has been asked in the question or is it something else?
 

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Answers and Replies

  • #4
tnich
Homework Helper
1,048
336

Homework Statement


Refer the image

Homework Equations


Equations for permutations and combinations

The Attempt at a Solution


Let x be the no. of questions that turned out to be correct. So total score will be 3x-(10-x)=4x-10.
The value of this expression must be from the given set and since x is an integer, the only no. satisfying the condition from the set is 18. (4(7)-10=18).
Hence 7 questions were correct and 3 incorrect. So, no. of ways of choosing 7 questions from 10 would be 10C7 = 120. Isn't this what has been asked in the question or is it something else?
Given that you have chosen 7 right answers and three wrong answers, how many ways are there to choose each of the 3 wrong answers?
 
  • #5
35,268
11,532
Given that you have chosen 7 right answers and three wrong answers, how many ways are there to choose each of the 3 wrong answers?
Ah, good point. That makes it 3240.
 
  • #6
Given that you have chosen 7 right answers and three wrong answers, how many ways are there to choose each of the 3 wrong answers?
Thanks I got it.
 

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