Question: Please explain each step in this discrete problem, and all parts. thank you. 9. (9pt) The diagram below shows the keypad for an automatic teller

Please explain each step in this discrete problem, and all parts. thank you.

9. (9pt) The diagram below shows the keypad for an automatic teller machine. As you can see, the same sequence of keys represents a variety of different strings. For instance, 2133 represents AZDE and BQFD). 1 2 3 Qz ABC DEF 4 5 GHI JKL MNO 7 8 9 PRS TUV WXY (a) How many different strings are represented by the same sequence of keys for 1234? (b) At a particular bank, each debit card is assigned a PIN number. This is a four digit numeric sequence that does not contain a 1 or a 0. How many possible PIN numbers are there? (e) How many different strings are represented by all of the available PIN numbers? (assume a PIN number is 4 digits and does not include a I or a ()

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