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- gyikooko
- Students
- Posts: 1
- Joined: Sun Jul 21, 2013 1:01 am
Combinatorics help
Can someone use an illustration to explain distinguishable and undistinguishable elements in the combinatorics strategy section? Thanks!
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: Combinatorics help
Hey Gyikooko,
The words don't have any meaning that is special for combinatorics. They just mean what they mean. If you're trying to figure out all the ways to scramble the word SWISS, the three S's are indistinguishable (there's no way to differentiate them). This means that some spellings are indistinguishable. Imagine that we see the 5 letters this way:
W
I
S1
S2
S3
Seen this way, the spellings S1 W I S2 S3 and S2 W I S1 S3 are indistinguishable, so they don't count as separate spellings.
Does that make sense?
-t
The words don't have any meaning that is special for combinatorics. They just mean what they mean. If you're trying to figure out all the ways to scramble the word SWISS, the three S's are indistinguishable (there's no way to differentiate them). This means that some spellings are indistinguishable. Imagine that we see the 5 letters this way:
W
I
S1
S2
S3
Seen this way, the spellings S1 W I S2 S3 and S2 W I S1 S3 are indistinguishable, so they don't count as separate spellings.
Does that make sense?
-t
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