How many possible 3 letter combinations are possible with alphabet?

Question

Ex: DEG CBE

Acronym of 3 with the alphabet, how many possible combinations?

Equation for this?

How could I set the possible answers up, like a stratified random sample?
ABC
ACB
BAC...

Answer 1

26 X 26 X 26
in cases such as these you essentially say you have a set amount of spaces (3 for you) and you have a certain number of things to fill these spaces (26 letters in alphabet). _X_X_ or filling in makes it 26 X 26 X 26, but if you dont want combinations like AAA or DDD then you take out one letter for each position 26 X 25 X 24. this takes out the one letter that you used per space. have fun

Answer 2

3 Letter Combinations

Answer 3

Well it actually depends on if the letters in the sequenceare allowed to repeat. if the letters are allowed to repeat in the sequence then you have 26^3 possible combinations or 17,576.

If you don't let letters in a sequence repeat, the your possible combitions is 26 x 25 x 24 or 15,600

The only way i can think about this is abstract, is there really an equation? ok, let's consider the first way, your choosing 3 letter out of a possible 26 in which repeat is allowed, so your combination formula is 26C3, in the second case, a letter in the sequence is not allowed to repeat so this is considered a pemutation or 26P3

Answer 4

17 576 three letter combinations (all upper or lower case)

This is really the same as counting from AAA to ZZZ:

AAA
AAB
AAC
.
.
.
AAZ
ABA

The maximum number of combinations is one plus
25*26^0 plus 25*26^1 plus 25*26^2 or
25[(26^0)+(26^1)+(26^2)]+1 =
25[1+26+676]+1 = 17 576

This is not hard to prove if you think of what you have as a base-26 number system counting from the lowest three digit combo to the highest three digit combo. The highest three digit combo plus one is the total count. Compare to counting to one thousand:

000 is analogous to AAA
999 is analogous to ZZZ
and don't forget to add one to get a thousand.

Substitute into the equation I used, but replace the 25 with 9 and the 26 with 10. You will see that you get one thousand as the answer.

Answer 5

Assuming all letters have to be different, then: 26 x 25 x 24 = 15,600.

Answer 6

If you can use the same letter more than once, it's:
26 * 26 * 26 = 17,576

If not, then:
26 * 25 * 24 = 15,600

Answer 7

stevetower's answer is right if letters can be repeated.

if not, 26•25•24 = 15,600 arrangements (permutations)

Answer 8

If length of 1 or 2 are included such as "E", "MJ", "UY", where the 27th "letter" you could call "Null", then it's 27^3.
But that would include Null in the middle ("H-S", "W-A") or as 1st letter ("--R", "-PX") which might not be desireable.

Answer 9

17,576 =26X26X26