Question

If the password can contain upper/lower case letters, digits, or any of eight special symbols: (Note: leave answers in exponent or simplified factorial form)

How many different 8-character passwords are possible if characters cannot be repeated?

Answer 1

Number of lower case letters = 26

Number of upper case letters = 26

Number of digits = 10

Number of special symbols = 8

total number of characters = 26+26+10+8 = 70

Number of different 8-character passwords from the available 70 characters with no repeated characters =

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First character of the password can be any of the 70 available characters;

As characters can not be repeated;

Second character can be any of the remaining 69 characters

third character can be any of the remaining 68 character .

.....

......

Eight character can be any of the remaining 63 characters;

Number different 8-character passwords that are possible if characters cannot be repeated =

70 x 69 x 68 x 67 x 66 x 65 x 64 x 63

= 3.80635E+14