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There are many situations in which a person is asked to create a PIN (Personal Identification Number) which may then be used to verify identity, for example, accessing an ATM requires a four-digit PIN and a six-digit PIN is used to access the A/V technology in many UW classrooms.
a. How many different 6-digit PINs are there?
b. How many different 7-digit PINs are there where none of the digits are repeated?

Respuesta :

Answer:

Step-by-step explanation:

(a)Different 6 -digit PIN's are

Every number from 0 to 9 can be filled in six slots of Pin therefore no of ways are

[tex]=10^{6}[/tex]

(b)No of & digit PIN's are

First number of Pin can be filled in 10 ways

second digit can be filled in 9 ways as repetition is  not allowed similarly last digit can be filled with 4 ways

total No of ways are[tex]=10\times 9\times 8\times 7\times 6\times 5\times 4=604800[/tex]

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