How Many Different 4 Letter Radio Station Call Letters Can Be Made

Found 2 solutions by jsmallt9, math-vortex:

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Reply by jsmallt9(3758) (Prove Source):

You can put this solution on YOUR website!

• In that location are only ii choices for the showtime letter of the alphabet: Thou or W
• Since repeats are allowed, there are 26 choices for the 2d letter
• Since repeats are allowed, there are 26 choices for the third alphabetic character
• Since repeats are allowed only "O" is not immune at the stop, there are only 25 choices for the 4th letter.

So in that location are 2*26*26*25 possible radio station telephone call letters. (I'll leave ti yous to multiply this out.)

Reply by math-vortex(648) (Bear witness Source):

You tin put this solution on YOUR website!

Hi, at that place--  The Problem:  How many different 4 letter radio station call messages 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 nosotros accept m ways of doing something  and northward means of doing another thing, then there are k � n ways of performing both actions.  We tin use this thought to solve your radio station trouble.  There are 2 ways to choose the get-go letter of the radios call sign; it must be either K or W. In that location are 26 means to choose the 2d alphabetic character because information technology can exist any letter (repeats are OK.) At that place are 26 ways to choose the third letter. In that location are 25 ways to cull the quaternary letter of the alphabet because it can be any alphabetic character but O. . Using the basic counting principle, we multiply, 2*26*26*25 = 33800  In that location are 33,800 means to choose the phone call letters.  Feel gratuitous to e-mail me if you take questions about the solution.  Ms.Figgy math.in.the.vortex@gmail.com            

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