Math Is Fun Forum

Stanley

Member

Registered: 2006-10-27

Posts: 9

What logic is to be used?

Hi,

How can this be computed? There are n different color balls and I pick m balls. What is the total possible combinations that can be expected? Note the balls may or may not repeat x times and the order is important.

Let me place this in example terms, In a sack of 8 different color balls, I am to pick four. What is the total possible combinations that can be expected?

For example let us say I picked 4 out of 8 Red Green Green Black and that is different from Black Green Green Red.

Thanks,
Stanley

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: What logic is to be used?

n^m

Now try to reason out why.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: What logic is to be used?

I think there is an unclear part of the question.

You say "the balls may or may not repeat" which gives us the idea that a color could be repeated multiple times (which Ricky has the answer for).

But then you give an example of "4 out of 8" ... you would need 4 balls of every color to allow for all possible repeats.

So, is there "replacement" ... ? Do the balls go back into the bag after choosing (or are there enough balls of every color)? If not, then it is important to know what is in the bag.

Read Combinations and Permutations

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Stanley

Member

Registered: 2006-10-27

Posts: 9

Re: What logic is to be used?

Hi Ricky & co,

Thanks for the quick answers, the link also explains very cool about Permutation with repetitions.

just to make thing clear, 4 out of 8, where 8 is the available colors, there are enough balls in the sack.

Best regards,
Stanley

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: What logic is to be used?

Then Ricky's answer is the right one!

8 possibilities for the first choice, 8 for the second, etc ... = 8 × 8 × 8 × 8

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: What logic is to be used?

8 7 6 5

eg: 2 out of 3-A,B,C
AB
AC
BA
BC
CA
CB
3*2=6

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X'(y-Xβ)=0

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: What logic is to be used?

George, there can be repeats:

AA
BB
CC

Which is 9 or 3*3.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: What logic is to be used?

I interpreted, each color, one ball.

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X'(y-Xβ)=0