Calculating Unique Permutations of 30 'A's and 30 'B's or 1s and 0s

[rsala004]

this problem has been on my mind...

how many permutations can you make with 30 'A's and 30 'B's

or rather the same question, how many unique numbers can be made from 30 1s and 30 0s

any ideas?
(excluding permutations that look identical)

thanks

 

[JSuarez]

Use permutations with repetition.

 

[dacruick]

it might be 60! / (30! x 30!)

 

[JSuarez]

It is.

 

[sutupidmath]

In general if we have say a sequence of n items and say k objects/elements are repeated s_j times correspondingly j=1,2,...,k, then the total nr. of permutations is:

n!/[(s_1)!*..*(s_k)!]

 

[awkward]

this problem has been on my mind...

how many permutations can you make with 30 'A's and 30 'B's

or rather the same question, how many unique numbers can be made from 30 1s and 30 0s

any ideas?
(excluding permutations that look identical)

thanks

Here is another way to look at the problem.

You have a sequence of 60 symbols; you choose 30 of them to be A's. (The others will be B's.) This can be done in
\binom{60}{30}
ways.