Suppose that you open an on line bank account account and...

. Suppose that you open an on-line bank account account and you are told that you must use a five-character password & each character must be alpha-numeric (either alphabetical or numerical). For the alphabetical characters you are required to use the English alphabet. Assume that a lower case letter is different from an upper case one. a) How many passwords are possible under these conditions? Give the exact answer as a number.

Transcript

00:01 All right, so we have this bank account.

00:02 You've got to make a password.

00:03 It's five characters long.

00:06 You can only use letters and numbers.

00:09 But then they say that you can only use the english alphabet, and a lowercase letter is different than an uppercase letter.

00:18 So that kind of gives you a few more options.

00:20 So the order does matter.

00:23 For example, if i put the password one, two, three, four, five in, well i could go five, four, three, two, one.

00:32 The order matters.

00:33 That's a different password.

00:35 Those are even though they're the same numbers.

00:38 So you need that because now the order matters.

00:41 That means we're going to do permutations for this.

00:46 And we can repeat.

00:48 You know, i could put one, one, one, one, one.

00:50 I could do that.

00:51 I could put, you know, a, a, a could repeat a a couple times if i wanted to.

00:56 All right.

00:56 So there's 26 letters in the english alphabet, and there's 10 numbers, if you go 0 through 9, that we can choose from, right? there's five, one, two, three, four, five numbers that we're going to, or five characters we got to pick.

01:20 Now, remember, for the letters, there's 26 of them, but there's 26 capital letters, and then there's 26.

01:31 Lowercase letters.

01:32 So there's actually 52 numbers to choose from.

01:36 All right.

01:37 So the options that i have for my first number, i can, for my first character, i can choose any of the 52 letters, upper lowercase letter, and any of the numbers.

01:52 So that's choice of 62.

01:55 Now when i go to the second character, i can still choose 62.

01:59 Third character, i can still choose 62.

01:59 Third character, i can still still choose 62, still choose 62, still choose 62, right? and then i just got to multiply all those together, okay? multiple them all together.

02:14 So on my phone here, on your calculator, i'm using my phone, that's just going to be 62 times 62 times 60 or 62 to the fifth.

02:26 I got, oh, wow, 916 million, 132 ,000, 132 ,000.

02:34 Thousand uh, 832.

02:41 So that should be how many different passwords you could come up with...

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