Password combinations, how many for these?

(i) A six-character password consisting only of lowercase letters

(ii) A six-character password consisting of only upper- and lowercase letters

(iii) An eight-character password consisting only of lowercase letters

(iv) An eight-character password consisting of only upper- and lowercase letters

(v) An eight-character password consisting of upper- and lowercase letters and at least one numeric digit (0–9)

(vi) A ten-character password consisting of upper- and lowercase letters and at least one numeric digit (0–9)

(vii) Explanation of Method Used for Calculation:

Can anyone help with these questions? I'm posting in privacy to get the best answers by some of you brainiacs. I'm not too good at math, it relates to a cracking project I''m doing.

Thanks in advance.

 

Hard to believe that none of the knowledgeable, and in many cases, brilliant, users who frequent these forum, have answered your questions.

Instead of answering your questions directly, let me try to tell you how to figure out the answers. It's really not all that difficult. Here goes.

Suppose I have a single, six-sided die, with the numbers 1 through 6 on the six sides. I roll that die. As will be apparent, there are 6 possible results; 1, 2, 3, 4, 5, or 6.

Now lets roll two of those same dice. The answer to "How many possible results?" is pretty easy to figure out. The first number of the first die can be matched with each of the 6 numbers of the second die to give six combinations (1-1, 1-2, 1-3, etc); the second number of the first die can similarly be matched with each of the six numbers of the second die to give six more combinations (2-1, 2-2, 2-3, etc.). Continuing with this same logic for all six sides of the first die, we arrive at the conclusion that we can have 6*6, or 36, possible combinations of the numbers on the two dice.

Applying the same logic, you will see that three six-sided dice can produce 6*6*6 (6^3 or 6 to the third power), i.e, 6*36, i.e., 216 combinations. Add another six-sided die, and the possible outcomes increases to 6*6*6*6, or 6^4, i.e., six to the fourth power.

Now you should have the answer to your questions:

-- A six character password from lower case letters can produce 26 (number of lower case letters)^6 combinations, or 308,915,776 combinations.

-- A six-character password consisting of only upper- and lowercase letters can produce 52 (number of upper and lower case letters) ^6, or 19,770,609,664 combinations.

I leave the rest to you.

__

 

Same here I read it initially, but nuked my reply. What are you asking?

PD