Problem

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 $\mathrm{W}$ or $\mathrm{K}$ and only the letters $J$ to $X$ ? (Count all possibilities even though, practically, some may be inappropriate.) There are four-letter sets that can be formed.

Solution

Step 1 :There are two choices for the first letter, which can be either W or K.

Step 2 :For the second letter, there are 10 choices from the letters J to X.

Step 3 :For the third letter, there are 9 choices left, since we can't repeat the second letter.

Step 4 :For the fourth letter, there are 8 choices left, since we can't repeat the second and third letters.

Step 5 :So the total number of four-letter sets is \(2 \times 10 \times 9 \times 8\).

Step 6 :Calculating this gives us a total of 1440 possible four-letter sets.

Step 7 :Final Answer: The total number of four-letter sets possible using either W or K and only the letters J to X is \(\boxed{1440}\).

From Solvely APP
Source: https://solvelyapp.com/problems/32080/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download