Question

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?

Answer 1

There are 1,000,000 different 6-digit PINs and 604,800 different 7-digit PINs where none of the digits are repeated.

Step-by-step explanation:

a. To calculate the number of different 6-digit PINs, we need to determine the number of options for each digit. Since there are 10 possible digits (0-9), each digit can be chosen in 10 different ways. Therefore, the total number of 6-digit PINs is 10^6 = 1,000,000.

b. To calculate the number of different 7-digit PINs where none of the digits are repeated, we need to determine the number of options for each digit. Since there are 10 possible digits (0-9) and no digit can be repeated, the number of options for the first digit is 10. For the second digit, there are 9 options left. The same goes for the third digit, and so on. Therefore, the total number of 7-digit PINs where none of the digits are repeated is 10 × 9 × 8 × 7 × 6 × 5 × 4 = 604,800.

Answer 2

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

`=10^(6)`

(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
`=10* 9* 8* 7* 6* 5* 4=604800`