Question

A system of identifying call letters uses call letters that begin either with E or W. Some have a total of 2 letters, and others have 3 letters. How many different call letters are possible?

Answer 1

Answer:

If repetition is allowed then the different call letters possible are 1404.

If repetition is allowed then the different call letters possible are 1250.

Step-by-step explanation:

The call letter are of either 2 letter or 3 letters.

And for them to be identified they should start with either E or W.

• If Repetition is allowed:

Consider the call letters with 2 letter:

Possible number of call letters starting with E : E _

The second place can be filled any of the 26 letters.

Possible number of call letters starting with W : W _

The second place can be filled any of the 26 letters.

Consider the call letters with 3 letter:

Possible number of call letters starting with E : E _ _

The second place and third place can be filled with any of the 26 letters.

Possible number of call letters starting with W : W _ _

The second place and third place can be filled with any of the 26 letters.

Total number of possible letters: 26 + 26 + (26)² + (26)² = 1404

Thus, if repetition is allowed then the different call letters possible are 1404.

• If Repetition is not allowed:

Consider the call letters with 2 letter:

Possible number of call letters starting with E : E _

The second place can be filled any of the 25 letters.

Possible number of call letters starting with W : W _

The second place can be filled any of the 25 letters.

Consider the call letters with 3 letter:

Possible number of call letters starting with E : E _ _

The second place can be filled with any of the remaining 25 letters and the third can be filled with the remaining 24 letters.

Possible number of call letters starting with W : W _ _

The second place can be filled with any of the remaining 25 letters and the third can be filled with the remaining 24 letters.

Total number of possible letters: 25 + 25+ (25 × 24) + (26 × 24) = 1250

Thus, if repetition is allowed then the different call letters possible are 1250.