Television and radio stations use four call letters starting

Television and radio stations use four call letters starting with W or K, such as WXYZ or KRLD. Assuming no repetitions in the second to fourth letters, how many four-letter sets are possible using either W or K, and only the letters C to U.

Solution

Case 1: The initial letter is an W

The first position can be filled in only one way, second position can be filled in remaininig 19 alphabets (from C to U)

The third position can be filled in remaining 18 ways

The fourth position can be filled in remaining 17 ways

Hence number of letters possible with W as the first character

=> 19 * 18 * 17 = 5814 ways

Case 1: The initial letter is an K

The first position can be filled in only one way, second position can be filled in remaininig 18 alphabets (from C to U) -{K}

The third position can be filled in remaining 17 ways

The fourth position can be filled in remaining 17 ways

Hence number of letters possible with K as the first character

=> 18 * 17 * 16 = 4896 ways

Total number of ways = 5814 + 4896 = 10710 ways