Combinations Question

C

calcnovis

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Mar 22, 2013
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I'm new to Statistics and I just want to verify I have the right answer.

I have 6 different dress colors, I wish to display 4 of them in my store. How many ways can 4 different colors be combined?

C(6,4)= 6!
4! (6-4)!

6.5.4! =5
4!.2!

Answer is 5

Am I doing this right?

Thanks in advance!
 
calcnovis said:
C(6,4)= 6!
4! (6-4)!
Click to expand...
Does the above mean "C(6, 4) = 6! / [4! (6 - 4)!]", as follows?

. . . . .\(\displaystyle \mbox{C}(6,\, 4)\, =\, \dfrac{6!}{4!(6\, -\, 4)!}\)

calcnovis said:
6.5.4! =5
4!.2!
Click to expand...
Do your decimal points above represent multiplication symbols (usually represented as "*" in textual form), as follows?

. . . . .\(\displaystyle \dfrac{6 \cdot 5 \cdot 4!}{4! \cdot 2!}\, =\, 5\)

Thank you! ;)
 
Hello, calcnovis!

I have 6 different dress colors. .I wish to display 4 of them in my store.
How many ways can 4 different colors be combined?

\(\displaystyle C(6,4)\:=\: \dfrac{6!}{4!(6-4)!} \:=\:\dfrac{6\cdot5\cdot4!}{4!\cdot2!} \;=\;5\) . Oops!
Click to expand...

Your last step is wrong.

\(\displaystyle \displaystyle \frac{6\cdot5\cdot\color{red}{\rlap{//}}4!}{\color{red}{\rlap{//}}4!\cdot2!} \;=\;\frac{\color{red}{\rlap{/}}6^3\cdot5}{\color{red}{\rlap{/}}2\cdot1} \;=\;3\cdot5 \;=\;15\)
 
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