Permutation and Combination

guest17

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Mar 24, 2012
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Can someone please help me out with this problem?

how many different combinations are there of 12 things, four of which are alike, if five are taken at a time?
I approached this question by calculating the possibilities with no restrictions, then dividing the 4 repeated items. I got (12C5)/4!...
 
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pka

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Jan 29, 2005
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how many different combinations are there of 12 things, four of which are alike, if five are taken at a time?
\(\displaystyle \[\sum\limits_{k = 0}^4 \dbinom{8}{5-k} \) HOW/WHY?
 

soroban

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Jan 28, 2005
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Hello, guest17!

I see no formula for this problem . . .


How many different combinations are there of 12 things,
four of which are alike, if five are taken at a time?

We have: .\(\displaystyle \{A, A,A,A, B,C,D,E,F,G,H,I\}\)
. . four A's and eight Others.

\(\displaystyle \begin{array}{ccccc} \text{0 A, 5 Others:} & _8C_5 &=& 56 \\
\text{1 A, 4 Others:} & _8C_4 &=& 70 \\
\text{2 A, 3 Others:} & _8C_3 &=& 56 \\
\text{3 A, 2 Others:} & _8C_2 &=& 28 \\
\text{4 A, 1 Others:} & _8C_1 &=& \;8 \\ \hline
\text{Total:} &&& 218\; \end{array}\)
 

guest17

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Thank you!
 
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