Mathematical Permutations

[The Kraken]

But as I asked at the outset . . . are the A's and E's discrete entities? And the answer was, yes.

Imagine, if you would, that you havve an array of little kids' alphabet blocks. This array consists of 7 blocks. However, in this array you have 2 "A" blocks and 2 "E" blocks. Even though they may be "indistinguishable" one from the other, they, nevertheless, constitute distinguishable members of the available combinations.

What one must consider, and what is the most important aspect of the problem, is the NUMBER of members in the array, not their identities.

You will note that the formula gives no consideration to the identities of the members, only their number and how many will be used in each combination.

the K

 

[mikemill]

One thing I've quickly learned: Don't expect that what a person says they want is really what they want.

 

[Cave Diver]

Given the following 7 letters

A A B C D E E

what is the maximum number of permutations using these letters??


My figuring says 3000 as there are

5 possibilities for the first letter A B C D or E .. (5)

assuming the first letter is an A
then there are 5 possibilities for the second letter A B C D or E .. (5 x 5)

assuming the second letter is an E
then there are 5 possibilities for the third letter A B C D or E ... (5 x 5 x 5)

then there are 4 possibilities for the fourth letter ... ( 5 x 5 x 5 x 4)


giving 5 x 5 x 5 x 4 x 3 x 2 x 1 = 3000 combinations

Is this correct ??? ... thanks

and am i correct in saying the minimum number would be 240?

Now do you want combinations or permutations?
Are the 2 A's and E's discrete entities?
Is the order of combination of importance?

the K

I *believe* what he is asking is that if you have only those letters to work with, how many unique combinations can they be arranged in.

i.e. A A B C D E E, A B A C D E E, A B C A D E E, A B C D A E E, etc.