Finding no. of combinations for the situation

[ubergewehr273]

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?

 

[mfb]

Looks right.

 

[ubergewehr273]

Looks right.

Well the answer is 3240

 

[tnich]

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?

 

[mfb]

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.

 

[ubergewehr273]

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.