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Q&A #725

Teachers' Lounge Discussion: One-to-one correspondence

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2003022120:01:54
Subject: Re: 1 to 1 correspondence

On 2003022114:42:18, Martin wrote:
>How do I solve how many different ways can you put a dozen eggs in
the
>carton? over 479 million? I do not understand how that answer was
>obtained	
>
There is quite abit of info re permutations; got to Google and search
on Permutations.

ab
ba        2

abc
acb
bac
bca
cab
cba       6 (3 permutations taken 3 at a time.)

abcd
abdc
acbd
acdb
adbc
adcb

bacd
badc
bcbd
bcdb
bdac
bdca

cabc
cacb
cbad
cbda
cdab
cdba

dabc
dacb
dbac
dbca
dcab    24 ((4 permutations taken 4 at a time.)


abcde
abced
abdce
abdec
abecd
abedc

and so forth.  If we finished, the number of permutations would be 120
for five permutations taken 5 at a time.    

The foumula is n! or n factorial.  12 factorial = 479,001,600.

The formula is nPr= n!
                  -----
                  (n-r)!  
But in this case r=n so that nPn=n! since 0!=1.

nPr is the number of permutations that can be made with n objects
taken r at a time.  

Most calculators have the nPr function built in.  You enter 12, push
the button and enter 12 and the result will be 479,001,600.





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