# Finding no. of combinations for the situation

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?

#### Attachments

• Screenshot-2018-5-27 master_A dvi - NEST2017_A pdf.png
34.5 KB · Views: 298

mfb
Mentor
Looks right.

Looks right.

tnich
Homework Helper

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
Mentor
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.

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.