#### eddy2017

##### Senior Member

- Joined
- Oct 27, 2017

- Messages
- 1,967

As part of his act, a magician has one red chip, one green chip, and one blue chip. He does a trick in which all three of those chips are placed in a row on a table. considering all possible arrangements of those chips, in how many of these arrangements will the red chip and green chip be side by side.

I have watched several videos on permutation and combination at my level.

I know that by going by the list option I can have the answer:

RBG -

so, taking a look at the options I realize that there are 4 arrangements of the type they ask for.

but then, I wonder that if I want to go the formula way, then I should go with

nPr = n!/ (n-r)!

but using this the result is 6.

my question is, is there any formula that might give me a direct solution, like, 4 in this case.

thank you,

eddy

Note: I edited the letters from Spanish to English.

I have watched several videos on permutation and combination at my level.

I know that by going by the list option I can have the answer:

RBG -

**RG**B - B**RG**- B**GR**- GAR -**GR**Bso, taking a look at the options I realize that there are 4 arrangements of the type they ask for.

but then, I wonder that if I want to go the formula way, then I should go with

nPr = n!/ (n-r)!

but using this the result is 6.

my question is, is there any formula that might give me a direct solution, like, 4 in this case.

thank you,

eddy

Note: I edited the letters from Spanish to English.

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