Math question

[Kami]

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In permutation I found two formulas that look similar but used differently. For example, if there are 2 pink balls, 3 white balls and 5 blue balls then how many three ball arrangements are possible. The solution is using the formula
n!/(n-r)!r! and the answer comes out to be 120.

OK so there is another formula that is n!/(n-r)! and what my question is that why can this formula not be applied. I have seen these two formulae being used but I wanted to clearify when to use the correct formula. Thanks in advance.

 

[DentalKitty]

The first formula is for Combinations (order doesn't matter). Some possibilities are considered the same, so the result is a smaller number. The second formula is for Permutations (order does matter). Each possibility is unique, so the answer is a larger number. Resident math whiz Streetwolf recommended that we assume order doesn't matter (Combinations) unless otherwise stated. I don't think I have seen him give a wrong answer so I'll just have to trust him 😛

 

[infernobutterfl]

In permutation I found two formulas that look similar but used differently. For example, if there are 2 pink balls, 3 white balls and 5 blue balls then how many three rose arrangements are possible. The solution is using the formula
n!/(n-r)!r! and the answer comes out to be 120.

OK so there is another formula that is n!/(n-r)! and what my question is that why can this formula not be applied. I have seen these two formulae being used but I wanted to clearify when to use the correct formula. Thanks in advance.

hmm.. dont want to be anal.. but the question states that you have different colored BALLS... and you want to arrange ROSE..... so its zero....

its kinda like saying... out of a group of only girls.. what are the odds of getting a boy girl, boy...

putting that aside...and assuming you mean balls instead of roses... is there a difference between each of the blue balls?

 

[Streetwolf]

hmm.. dont want to be anal.. but the question states that you have different colored BALLS... and you want to arrange ROSE..... so its zero....

its kinda like saying... out of a group of only girls.. what are the odds of getting a boy girl, boy...

putting that aside...and assuming you mean balls instead of roses... is there a difference between each of the blue balls?

Yes there is a difference. You can choose the first one, or the second one, or... etc.

Here's a situation where order matters (and you must figure that out from the problem description):

You have 10 grand prize finalists and you will randomly draw the 3 winning names from a jar. The first name is the grand prize winner and will receive $10,000. The second name gets the first prize for $3,000. The third name gets the second prize for $1,000. How many different ways can you pick the winners?

 

[Kami]

Thanks for letting me know about the rose. I changed it to balls.

 

[Lonely Sol]

Yes there is a difference. You can choose the first one, or the second one, or... etc.

Here's a situation where order matters (and you must figure that out from the problem description):

You have 10 grand prize finalists and you will randomly draw the 3 winning names from a jar. The first name is the grand prize winner and will receive $10,000. The second name gets the first prize for $3,000. The third name gets the second prize for $1,000. How many different ways can you pick the winners?

What about if the problem just said, 1st, 2nd and 3rd, order would still matter right, since only one person can be 1st, same with 2nd and so on!

 

[Streetwolf]

Yes, if it matters which person is picked first, second, third, etc then order matters.

Order matters: You need to select three winners out of 15 for a prize. The first name you pick is awarded the highest prize, the second name gets the next highest prize, and the third name gets the third highest prize.

Order doesn't matter: You need to select three winners out of 15 for a prize. The prize is the same for all three winners.

Order matters: You have 10 people and want to choose 4 of them to line up against a wall. The first person will stand to the left and each subsequent person will stand to the right of the last person.

Order doesn't matter: You have 10 people and want to choose 4 of them to line up against a wall, from tallest to shortest.

Order matters: You play the evening pick-4 lottery (except we'll pretend the numbers can't be repeated).

Order doesn't matter: You play the Mega Millions lottery or Power Ball or anything of that nature.

 

[DentalKitty]

Yes there is a difference. You can choose the first one, or the second one, or... etc.

Here's a situation where order matters (and you must figure that out from the problem description):

You have 10 grand prize finalists and you will randomly draw the 3 winning names from a jar. The first name is the grand prize winner and will receive $10,000. The second name gets the first prize for $3,000. The third name gets the second prize for $1,000. How many different ways can you pick the winners?

So would the answer be 10P3=720 then?

 

[Streetwolf]

Yeah.