Question

Problem 1. Assume a password in a computer system contains eight character, each can be a digit (0 to 9), an uppercase English alphabet, or a lowercase English alphabet. How many password are there

(a) if letters can be repeated? (b) if no letter can be repeated?

(c) starts with X and letters can be repeated?
(d) either starts with X or ends with 10 (letters can be repeated)?

(e) neither starts with X nor ends with 10 (letters can be repeated)?

Answer 1

Upper case english alphabet=26 letters

lower case english alphabet=26letters

from digit 0-9=10 digits

so total a password can be created from 26+26+10=62 letters.

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A) if letters can be repeated ,

Given a password can have 8 characters

so there are=(62)^8 passwords

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B)if no letter is repeated

then first letter will be chosen from 62 letters.

Second letter will be chosen from 61 letters.

third letter will be chosen from 60 letters and so on

so total passwords will be =(62)*(61)*(60)*(59)*(58)*(57)*(56)*(55)

= 1.3632589e+14 passwords.

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C)starts with X and letters can be repeated?

if it starts with X then the sequence of passwords will be X _ _ _ _ _ _ _

so the 2nd letter can be chosen from 62 letters.

so the third letter can also be chosen from 62 letters and so on

so total number of passwords =(1)*(62)*(62)*(62) *(62) *(62)*(62)*(62)

=(62)^7 passwords

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