Combination with repetition

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October 17th 2011, 03:28 PM
mybrohshi5

Combination with repetition

8 identical blackboards are divided among 4 schools:

1) what are the # of divisions possible?

using combination with repetition formula $\binom{n+k-1}{n-1}$

I get $\binom{8+4-1}{4-1} = \binom{11}{3}$

2) how many divisions are possible if each school receives at least 1 blackboard?

$\binom{8-1}{4-1} = \binom{7}{3}$

NOW FOR MY QUESTION:

I was curious to what would happen if it was asked: how many divisions are possible if each school receives at least 2 blackboards?

would it just be:

$\binom{8-2}{4-1} = \binom{6}{3}$

Thanks for any input :D
October 17th 2011, 03:40 PM
Plato

Re: Combination with repetition

Quote:

Originally Posted by mybrohshi5

8 identical blackboards are divided among 4 schools: 1) what are the # of divisions possible?
using combination with repetition formula $\binom{n+k-1}{n-1}$ I get $\binom{8+4-1}{4-1} = \binom{11}{3}$

2) how many divisions are possible if each school receives at least 1 blackboard?
$\color{red}\binom{8-1}{4-1} = \binom{7}{3}$

The answer for 2) should be $\binom{4}{3}$
October 17th 2011, 03:44 PM
mybrohshi5

Re: Combination with repetition

Not to question your knowledge, but are you sure?

My probability solutions guide (and the back of my book) says it should be 35 which is 7 choose 3...
October 17th 2011, 03:53 PM
Plato

Re: Combination with repetition

Quote:

Originally Posted by mybrohshi5

Not to question your knowledge, but are you sure? My probability solutions guide (and the back of my book) says it should be 35 which is 7 choose 3...

Look, if each school gets at least one then that leaves only four to give out. Whoever wrote the solutions manual is just simply wrong.
October 17th 2011, 03:59 PM
mybrohshi5

Re: Combination with repetition

That sounds good to me. Thank you!

So if it was at least 2 blackboards given to each school, that means that NO blackboards are left to give out so would that just be 1?

And do you mind if I ask you about a similar problem dealing with people exiting an elevator?

I am studying for my midterm exam tomorrow and am really trying to understand combination problems.
October 17th 2011, 04:18 PM
Plato

Re: Combination with repetition

Quote:

Originally Posted by mybrohshi5

And do you mind if I ask you about a similar problem dealing with people exiting an elevator?

Not at all.
But by forum rules post in a new thread.