Finding no. of combinations for the situation

In summary, the conversation discusses solving a problem using permutations and combinations. The value of an expression is determined to be 18, and it is found that there are 7 correct and 3 incorrect answers. The question is posed about choosing 3 wrong answers, leading to the final answer of 3240 ways.
  • #1
ubergewehr273
142
5

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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  • #3
mfb said:
Looks right.
Well the answer is 3240
 
  • #4
ubergewehr273 said:

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
tnich said:
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
tnich said:
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.
 

Related to Finding no. of combinations for the situation

1. How do you calculate the number of combinations for a given situation?

To calculate the number of combinations, you need to use the formula nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items in each combination.

2. Can you give an example of finding the number of combinations?

Sure, let's say you have 10 different toppings to choose from for your pizza, and you can only choose 3 toppings. The number of combinations would be 10C3 = 10! / (3! * (10-3)!) = 120.

3. What is the difference between combinations and permutations?

Combinations are a way to choose a group of items from a larger set, where the order of the items does not matter. Permutations, on the other hand, involve arranging the items in a specific order.

4. Is there a limit to the number of combinations that can be calculated?

Theoretically, there is no limit to the number of combinations that can be calculated. However, as the numbers get larger, it may become impractical to calculate them manually without the use of a calculator or computer.

5. How can the number of combinations be useful in real-life situations?

The concept of combinations is commonly used in fields such as statistics, probability, and genetics. It can also be applied in everyday scenarios, such as choosing outfits from a wardrobe or creating different meals from a set of ingredients.

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