Question 623665: How many different 4 letter radio station call letters can be made if the first letter must be K or W, repeats are allowed, but the call letters cannot end in an O? please explain.
Found 2 solutions by jsmallt9, math-vortex:
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! - There are only 2 choices for the first letter: K or W
- Since repeats are allowed, there are 26 choices for the second letter
- Since repeats are allowed, there are 26 choices for the third letter
- Since repeats are allowed but "O" is not allowed at the end, there are only 25 choices for the 4th letter.
So there are 2*26*26*25 possible radio station call letters. (I'll leave ti you to multiply this out.)
Answer by math-vortex(648)  (Show Source):
You can put this solution on YOUR website!
Hi, there--
The Problem:
How many different 4 letter radio station call letters can be made if the first letter must be K or W,
repeats are allowed, but the call letters cannot end in an O?
.
A Solution:
In combinatorics, the basic counting principle states that if we have m ways of doing something
and n ways of doing another thing, then there are m · n ways of performing both actions.
We can use this idea to solve your radio station problem.
There are 2 ways to choose the first letter of the radios call sign; it must be either K or W.
There are 26 ways to choose the second letter because it can be any letter (repeats are OK.)
There are 26 ways to choose the third letter.
There are 25 ways to choose the fourth letter because it can be any letter but O.
.
Using the basic counting principle, we multiply,
2*26*26*25 = 33800
There are 33,800 ways to choose the call letters.
Feel free to email me if you have questions about the solution.
Ms.Figgy
math.in.the.vortex@gmail.com
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