Math Is Fun Forum

chetah

Member

Registered: 2008-02-15

Posts: 32

Combinations

consider the collection of all strings of length 10 made up from the alphabet 0, 1,2 and 3.  How many of these strings have weigth 3?  How many have weight 4?  How many have even weight?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Combinations

Weight = 3:
1110000000 mix it up, maybe 120?? It's a guess with formula not sure.
2100000000 mix it up. maybe 90?? I'm guessing with a formula I don't know.
3000000000 mix it up. maybe 10?  Yes, this is right.
Add all those up.  120 + 90 + 10 = 220
Answer: 220 with weight 3, maybe?

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Combinations

Weight = 4:
1111000000 mix it up: maybe 210, but I don't know.
2110000000 mix it up: maybe 360, but not sure.
3100000000 mix it up: maybe 90, but not sure.
4000000000 mix it up: there are 10 of these, yes.
Add all those up: 210 + 360 + 90 + 10 = 670
Answer: 670 with weight 4, maybe?

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Combinations

Even Weights:
Weights can vary from zero if all zeros, to 30 if all 3's.
So all string permutations is 4^10.
So even ones is probably half of this.
Answer: 524288 maybe.

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igloo myrtilles fourmis