How many combinations of o and e 8 digits long can you make?

Question

Is there a formula because I would also like to know how many combination of o and e 10 digits long. 

Answer 1

For each digit _ _ _ _ _ _ _ _ there are two options only. If there were 2 digits only, you would have 4 combinations: ee, oo, eo, oe. If there were 3 slots, you would have 8 combinations. Every time you add a slot, you double the number of combinations.

 

 The formula here is 2^k= # of combinations.  k is the number of digits. Mind you this works because there are two choices and I'm assuming the order matters. In other words, something like eeeoe and eoeee are not the same. 

 

For any number of choices (a) and digits(k), the # of combinations = a^k 

These ordered combinations are called permutations and the easy formula works because you can repeat the letters as many times as you want.