An Internet service provider requires its customer to select a password consisting of four letters followed by three digits. Find how many such passwords are possible in each of the following cases:

(a)	Repetition of letters and digits is allowed.
(b)	Repetition of letters and digits is not allowed.

(a)

To find:

The number of passwords which can be created when repetition of letters and digits is allowed.

Approach:

The Fundamental counting principle states that “For any number of events E1,E2,.....,En occurs in n1,n2,....,nn number of ways, then the whole event can occur in n1×n2×....×nn ways.”

The number of ways in which the password can be created is given by,

Number of ways=n1×n2×n3×n4×n5×n6×n7 ...(1)

Given:

The password has first four units as letters and the next three units as digits. Repetition is of letters and digits are allowed.

Calculation:

Number of letters are 26 and number of digits are 10

(b)

To find:

The number of passwords which can be created when repetitions of letters and digits is not allowed.