Question

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 upper f to upper x​? ​(count all possibilities even​ though, practically, some may be​ inappropriate.)

Answer 1

Here we are dealing with combinations without repetitions.

Let's write the form of a name.
For names starting with W:
W _ _ _
For names starting with K:
K _ _ _

We are allowed to use only lettrs from F to X. That's total of 19 letters. We are not allowed to repeat letters so for each letter we can choose from one less available letters.

Let's start with names begining with W. We will write how man possible letters we can choose from.
W 18 17 16
At second possition we can choose from 18 letters because we must not repeat letters and W is placed in front of X in alphabet.
At third position we can choose from 17 letters becasue we already chose two of 19 possible letters.
At fourth position we can choose from 16 letters becasue we already chose three of 19 possible letters.
To calculate total number of possible names we need to multiply these numbers:
1 * 18 * 17 * 16 = 4896

Same calculation can be done for names starting with K. We would get same number as solution.

Total number of possible names starting with W or K is 4896 + 4896 = 9792