Coin permutation/combination problem

[RearAdmiral]

Say you have a letter on each side of a coin:
26 letters=13 coins total.

You draw 7 coins out of the 13 total each draw. How many 7 letter combinations can you get in total with your 13 coins?

I haven't done this kind of math in a loooooong time. I don't remember how to deal with using two sides of an object in this type of problem.

I initially had setup an (n-2) type formula instead of (n-1). Something like

((26)(24)(22)(etc))
over
12! * (26-12)!

Got 9 million something but not sure if that's right. I assume this is all wrong.

Thanks for any help gang.

 

[FelixDeCat]

I dont know the answer to your question, but I noticed you mentioned the phrase "each draw". How many draws will occur? And what if you dont draw any vowels?

 

[summit]

i think this is how you do it, one coin is 2^1, two coins should be 2^2, and three coins should be 2^3. so 7 coins should be 2^7.

 

[RearAdmiral]

I dont know the answer to your question, but I noticed you mentioned the phrase "each draw". How many draws will occur? And what if you dont draw any vowels?

Well I just wanted to make clear that you only got 7 coins at a time. "Word" is just any combination of 7 letters. Doesn't need to be an actual word.

There really isn't an amount of draws variable, just tried to make the problem clear.

 

[RearAdmiral]

i think this is how you do it, one coin is 2^1, two coins should be 2^2, and three coins should be 2^3. so 7 coins should be 2^7.

But you have to take the 13 total coins into consideration.

 

[Schfifty Five]

Well I just wanted to make clear that you only got 7 coins at a time. "Word" is just any combination of 7 letters. Doesn't need to be an actual word.

There really isn't an amount of draws variable, just tried to make the problem clear.

You should change the OP then. Using the the word "Words" is confusing. Should just say something like "How many 7 letter combinations can you make?"

 

[Safeway]

It isn't 2^7 ...

1 coin, A/B, you can have 2 variations -

A B

2 coins, A/B and C/D, you can have 8 variations -

AC AD BC BD
CA DA CB DB

3 coins, A/B and C/D and E/F, you can have 48 variations -

Order: 1, 2, 3 - 8 variations
Order: 1, 3, 2 - 8 variations
Order: 2, 1, 3 - 8 variations
Order: 2, 3, 1 - 8 variations
Order: 3, 1, 2 - 8 variations
Order: 3, 2, 1 - 8 variations

Headed home, think on it.

 

[DrPizza]

13P7 times 2^7. There are 13*12*11*10*9*8*7 different orders for the coins. For each order, there are 2^7 different ways the coins can be flipped. (think of them as buttons that are on or off, or think of it in binary - every coin represents a 0 or a 1. Heads is a 0, tails is a 1. You can have everything from 0000000, 0000001, 0000010,... to 1111110,1111111. A total of 128 ways to flip the 7 coins for any specific order.

 

[DrPizza]

You should change the OP then. Using the the word "Words" is confusing. Should just say something like "How many 7 letter combinations can you make?"

Except that would be even more wrong, since in mathematics, a combination is much different than a permutation. i.e. If you said "put any combination of 3 animals into a car," someone could stick in a cat, then a dog, then a goat. That would be the same combination of 3 animals as putting in a goat first, then cat, then dog. In a permutation (or word), the order of the letters matters. wxr is a word. xwr is a word. Neither is a word in the English language, but both are "words."

 

[Exterous]

The other coin is a nickle.

Wait...what?

 

[RearAdmiral]

13P7 times 2^7. There are 13*12*11*10*9*8*7 different orders for the coins. For each order, there are 2^7 different ways the coins can be flipped. (think of them as buttons that are on or off, or think of it in binary - every coin represents a 0 or a 1. Heads is a 0, tails is a 1. You can have everything from 0000000, 0000001, 0000010,... to 1111110,1111111. A total of 128 ways to flip the 7 coins for any specific order.

Makes sense. Looks good to me. We shall see if this is the correct answer!

 

[RearAdmiral]

The other coin is a nickle.

Wait...what?

lol

 

[DrPizza]

Makes sense. Looks good to me. We shall see if this is the correct answer!

It's the correct answer to the *original* question posed at the top of the thread. I cannot guarantee that the question in the OP has been copied perfectly from the original question. The answer to the reworded question is actually different than the answer to the original question. Mathematically, there's a huge difference between "word" (meaning a string of letters in a certain order) and "combination." Dog and God are the same combination of letters from the alphabet (mathematically speaking), but different permutations of those 3 letters. A combination lock is really a permutation lock, since 1 - 2 - 3 won't open a lock whose "combination" is 3 - 1 - 2.

 

[gophins72]

hmmm since i'm late to the party i will just say:

1...2...3. 3 licks to get to the center of a tootsie roll lollipop.

 

[FelixDeCat]

No one has answered my question. What happens if no vowels are drawn? You said "words" not jibberish. Or is it possible to factor something like that? Probabilities?

 

[Juked07]

Agree immediately with DrPizza's solution, and his definition of "word" in the mathematical sense.

EDIT: Felix, the way mathematicians use "word" takes care of your concern. No vowels are needed to make a word.

 

[FelixDeCat]

Agree immediately with DrPizza's solution, and his definition of "word" in the mathematical sense.

EDIT: Felix, the way mathematicians use "word" takes care of your concern. No vowels are needed to make a word.

Ill agree with you if you can show me a few words with no vowels.

 

[Safeway]

Scrabble Words - No Vowels, No Y

BRR
BRRR
CRWTH
CRWTHS
CWM
CWMS
HM
HMM
MM
NTH
PFFT
PHPHT
PHT
PSST
SH
SHH
TSK
TSKS
TSKTSK
TSKTSKS

Scrabble Words - No Vowels, Using Y

BY
BYRL
BYRLS
BYS
CRY
CRYPT
CRYPTS
CYST
CYSTS
DRY
DRYLY
DRYS
FLY
FLYBY
FLYBYS
FLYSCH
FRY
GHYLL
GHYLLS
GLYCYL
GLYCYLS
GLYPH
GLYPHS
GYM
GYMS
GYP
GYPS
GYPSY
HYMN
HYMNS
HYP
HYPS
LYMPH
LYMPHS
LYNCH
LYNX
MY
MYRRH
MYRRHS
MYTH
MYTHS
MYTHY
NYMPH
NYMPHS
PLY
PRY
PSYCH
PSYCHS
PYGMY
PYX
RHYTHM
RHYTHMS
RYND
RYNDS
SCRY
SHY
SHYLY
SKY
SLY
SLYLY
SPRY
SPRYLY
SPY
STY
STYMY
SYLPH
SYLPHS
SYLPHY
SYN
SYNC
SYNCH
SYNCHS
SYNCS
SYNTH
SYNTHS
SYPH
SYPHS
SYZYGY
THY
THYMY
TRY
TRYST
TRYSTS
TYPP
TYPPS
TYPY
WHY
WHYS
WRY
WRYLY
WYCH
WYN
WYND
WYNDS
WYNN
WYNNS
WYNS
XYLYL
XYLYLS
XYST
XYSTS

 

[Juked07]

Lol I guess safeway is all over that request, although it has nothing to do with the original math problem.

 

[Possessed Freak]

Safeway, you need to trim that list. No double letters possible, no ability to pull certain adjacent letters (can't have A *and* B in it).

 

[sdifox]

Safeway, you need to trim that list. No double letters possible, no ability to pull certain adjacent letters (can't have A *and* B in it).

he's just responding to the words without vowel comment. Not addressing op's question.

 

[RearAdmiral]

It's the correct answer to the *original* question posed at the top of the thread. I cannot guarantee that the question in the OP has been copied perfectly from the original question. The answer to the reworded question is actually different than the answer to the original question. Mathematically, there's a huge difference between "word" (meaning a string of letters in a certain order) and "combination." Dog and God are the same combination of letters from the alphabet (mathematically speaking), but different permutations of those 3 letters. A combination lock is really a permutation lock, since 1 - 2 - 3 won't open a lock whose "combination" is 3 - 1 - 2.

This makes me laugh as the original question had a lot of quotation marks such as find the number of "words." It wasn't a very technically written question. The order doesn't matter and it can be jibberish.