The following diagram shows the keypad for an automatic teller machine. As you can see, the same sequence of keys represents a variety of different PINs. For instance. 2133, AZDE. and BQ3F are all keyed in exactly the same way.
a. How many different PINs are represented by the same sequence of keys as 2133?
b. How many different PINs are represented by the same sequence of keys as 5031?
c. How many different numeric sequences on the machine contain no repeated digit?
(a)
The number of different PINs represented by the same sequence of keys as
Given information:
From the keypad shown, we understand that the button containing
Concept used:
The number of different pins, which represent the same sequence of keys as
Calculation:
Similarly, the key containing
(b)
The number of different PINs are represented b the same sequence of keys as
(c)
The number of numeric sequences that contain no repreated digit.