MHB Combination/probability question (High School level)

[Micky1964]

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

 

[romsek]

With your method groups with 3 girls get counted 3 times each rather than once each.

 

[Micky1964]

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

 

[romsek]

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.

 

[HOI]

I think it odd that choosing students "to represent the class in a debate" would be done at random!

 

[topsquark]

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

 

[HOI]

Yeah, I dropped out in the fourth grade!