Maths: Choosing

demon8991

demon8991

demon8991

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Got a questions which im doing just wanna check ive done it right.

'Springfield football club plan to field a team of 3 forwards, 4 mid fielders, 3 defenders and 1 Goal Keeper. Assuming they have 8 forwards, 6 mid fielders, 5 defenders and 2 goalkeepers on their books how many teams can they make.

This is how i did it.

8 choose 3 = 56, 6 choose 4 = 15, 5 choose 3 = 10, 2 choose 1 = 2

Now im not sure whether i times them together or add them together to get the amount of teams that can be made.

Any of you lot know?

Thanks

*EDIT*

'Determine the number of visually distinct that p red balls and q blue balls can be placed in a line.'

also

'Determine the number of ways that n = p + q + r objects can be divided into three groups with the first containing p objects, the second q, and the third r'

Thanks in advance for you help guys i really wanna get my head round all this.
 
Last edited:
“2 goalkeepers on their books how many teams can they make.”
Perhaps I am looking at this from the wrong point of view but if you have to have 1 goalkeeper per team and you only have 2 goalkeepers you can only make a max of 2 teams. Assuming there is a minimum of everything else for 2 teams, if there is not then 1 team is max.
 
It's been a couple of years since i've done this but i think it's:

(2C1) x (5C3) x (6C4) x (8C3) = i'll let you work it out :p
 
Haha i dont think it is a trick question though as we are just getting the basics of this they woulndt trick us yet i dont think.

But you never know.
 
demon8991 said:
Haha i dont think it is a trick question though as we are just getting the basics of this they woulndt trick us yet i dont think.

But you never know.
Click to expand...

Maybe they are trying to teach you to read the question properly. :)
 
Lol this is tiring i have doing maths all day, since 11 o clock, im determined to pass this year.

Ok moving on, im struggling with some algebraic diviations of this.

'Determine the number of visually distinct that p red balls and q blue balls can be placed in a line.'

also

'Determine the number of ways that n = p + q + r objects can be divided into three groups with the first containing p objects, the second q, and the third r'

Thanks in advance for you help guys i really wanna get my head round all this.
 
For the first question, people who have suggested "you can only have two teams" are probably interpreting the question wrong - it (absolutely definately) means "How many different ways could you choose a team?", rather than "How many teams can you have at once?". Doing it in any other way wouldn't get you any marks if it was an exam question.
 
For the question about arranging p blue balls and q red balls into visually distinct lines:

You have a total of p+q places that you can put balls into. If you fill up p of those places with the blue balls, then however you put the red balls into the remaining spaces, the arrangements will all look the same.

So we only need to think about how many ways there are of putting p blue balls into p+q spaces.

Can you do the rest?
 
demon8991 said:
Hmm ok i see does that mean that the answer is:

P!/(P+Q)!
Click to expand...
Well, no, because that number isn't an integer - the denominator is bigger than the numerator!

You might have meant to say (p+q)!/q! in which case you'd be nearly there. This is the number of ways of putting p balls into p+q spaces. However, you then have to consider that all of these ways look the same, since the balls are all the same colour...
 
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