Combination/probability question (High School level)

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In summary, the conversation discusses different approaches to a counting/probability problem involving boys and girls. The correct method involves treating each situation separately and avoiding multiple counting. It is also mentioned that choosing students to represent the class in a debate seems odd to be done at random.
  • #1
Micky1964
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Hi all. I'm doing a counting/probability problem here.
I can see how the correct answer for part b is arrived at by counting the number of combinations for "2 girls" then counting the number of combinations for "3 girls" , and adding these results.
But I've attached my first way of approaching it, which is wrong. Wondering if anyone can tell me why my approach doesn't give the correct answer. I know it's probably something obvious that I'm missing.
Thanks
 

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  • #2
With your method groups with 3 girls get counted 3 times each rather than once each.
 
  • #3
romsek said:
With your method groups with 3 girls get counted 3 times each rather than once each.
Thank you for replying. I can see that makes sense now.

So the best approach with these types of problems is to treat each situation separately? ie. find how many ways you can have 2 girls and 1 boy, then find how many ways you can have 3 girls and 0 boys, then add the 2 figures?

Mick
 
  • #4
Micky1964 said:
Thank you for replying. I can see that makes sense now.

So the best approach with these types of problems is to treat each situation separately? ie. find how many ways you can have 2 girls and 1 boy, then find how many ways you can have 3 girls and 0 boys, then add the 2 figures?

Mick

It's a bit difficult to cite any approach as "best" given the variety of problems that exist but generally separating the cases helps ensure you won't multiply count specific situations.
 
  • #5
I think it odd that choosing students "to represent the class in a debate" would be done at random!
 
  • #6
Country Boy said:
I think it odd that choosing students "to represent the class in a debate" would be done at random!
You clearly never went to my High School.

-Dan
 
  • #7
Yeah, I dropped out in the fourth grade!
 

FAQ: Combination/probability question (High School level)

What is the difference between combination and permutation?

Combination is the selection of objects without regard to order, while permutation is the selection of objects with regard to order.

How do I calculate the number of combinations or permutations?

The formula for combinations is nCr = n! / r!(n-r)!, where n is the total number of objects and r is the number of objects being selected. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects being selected.

What is the difference between with replacement and without replacement?

With replacement means that an object can be selected more than once, while without replacement means that an object can only be selected once.

How do I know when to use combinations or permutations in a problem?

Combinations are used when the order of the objects does not matter, such as selecting a group of people to be on a committee. Permutations are used when the order of the objects does matter, such as arranging a group of people in a line.

Can you give an example of a real-life situation where combinations or permutations are used?

A real-life example of combinations is when a lottery is drawn, as the order of the numbers does not matter. An example of permutations is when a race is run, as the order in which the runners finish matters.

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