i'm a bit rusty with my statistics/combinatorics. Can somebody show me the math behind this problem:

suppose you have 4 letters: A, B ,C, and D. each letter can be uppercase or lowercase. How many different ways can you write the four letters if they must stay in the same order (ie, order doesn't matter)
for example, some possibilities would be: ABCD, abcd, aBcD, ABCd, etc.

Question

i'm a bit rusty with my statistics/combinatorics. Can somebody show me the math behind this problem:

suppose you have 4 letters: A, B ,C, and D. each letter can be uppercase or lowercase. How many different ways can you write the four letters if they must stay in the same order (ie, order doesn't matter)
for example, some possibilities would be: ABCD, abcd, aBcD, ABCd, etc.

ggrree · Answer

another example of what I mean. Imagine you have letters A, B, a, b. how many ways could you arrange them?
in this example it's easy to count them out: AB, Ab, and ab. we only have 3 ways to write them.
am I clear?

ggrree · Answer

sorry, think I figured it out. the answer is 2^n, where n is the number of letters you have, since you've only got two choices (upper or lowercase) for each letter.