#How could I get the answer for this

68 messages · Page 1 of 1 (latest)

drowsy lion
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Carol has 4 different marker colors. How many ways can Carol create a box of 6 markers? The thing says it’s 84, however none of the formulas for combinations I know get that (and Google isn’t much help) . How would I derive this answer, and is there some formula for x different colors and y markers (I could probably just brute force but for time’s sake a formula would be better)

jagged islandBOT
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  1. Wait patiently for a helper to come along.
  2. Once someone helps you, say thank you and close the thread with: ```diff
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quasi anchor
lofty geyser
lofty geyser
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Check your book on permutations

quasi anchor
lofty geyser
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We just need to find out in how many ways of 6 we can mix them

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So one way will be let's say blue, blue, blue, blue, blue, blue

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Another will be red,red,red,red,red,red

quasi anchor
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ohh

lofty geyser
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So now

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How many combinations can we make

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Idk that

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Do you know

quasi anchor
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so this is a combination problem not a permutation problem

lofty geyser
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Idk the difference

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Haven't studied that

quasi anchor
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in combination order doesn't matters, for example ab and ba are considered the same
in permutation order matters, so for example ab and ba are considered different

lofty geyser
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Oh okay

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Makes sense

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So isnt this a permutation

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Order matters

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Blue,red,blue,blue,blue,blue

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And red,blue,blue,blue,blue,blue

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This is different

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Wait

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idk

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This is a combination okay

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I understand

quasi anchor
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yea it's combination in my opinion

lofty geyser
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Ye

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So how many can there be

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No

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It's a goddamn permutation

quasi anchor
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how?

lofty geyser
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Lemme think

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My gut says permutation

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Not my brain

quasi anchor
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it just says mix

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so order doesn't matter

lofty geyser
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Yea

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It's a combination

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So how do you solve this

quasi anchor
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I actually know a formula

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for combination with repetition

lofty geyser
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Which is?

quasi anchor
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C(n,r) = (n+r-1)!/r!(n-1)!
here n = 4, and r = 6

lofty geyser
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Hm

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Lemme solve it

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,w 9!

odd brookBOT
lofty geyser
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Well

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Wait

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,w 9!/(6!(3!))

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no

odd brookBOT
lofty geyser
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OH YAH

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It's 84

quasi anchor
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yea as OP said

lofty geyser
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Yep

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@drowsy lion swindle got your formulae+answer

drowsy lion
vapid sableBOT
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@drowsy lion has given 1 rep to @quasi anchor

drowsy lion
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+close