# Imortant and timely question for me.

#### DanoDragon

##### New member
I feel like an idiot for asking but I have never got this concept down. I would appreicate any help on this question.

"Many radio stations in the US have call letters that begin with a W or K and have four letters.

a) How many arrangements of four letters are possible as call letters?

b) What is the probability of having call letters KIDS?

I do want the answer but what I really need is information on holw to solve tis problem.

Thanks out there,

Danny

#### morson

##### Full Member
Possibilities:

W _ _ _

K _ _ _

If it started with a W, then in the second letter, there's 25 letters to pick from, making 24 letters to pick from in the next, and 23 letters to pick from in the next. So 25.24.23 arrangements, no? That's assuming you can't use the same letter repeatedly! If you can, there's $$\displaystyle 26^3$$ possiblities if it started with W. Then I suppose you'd just double the amount of arrangements if you want to consider the case for k being the first letter.

For your second question, the chance of something happening is the number of ways it can occur divided by the total number of outcomes (above paragraph).

#### Random

##### New member
Are they talking about calling numbers like 1-800-234-KDCA or the station name? There is a big difference.

#### DanoDragon

##### New member
See, here's the thing. This is for an elementary class that doesn't use exponentials. So, this answer seems too large. I'm in a teaching class that is showing us how to teach students and on this topic I am lost. In this text large numbers have not been included so I feel I have missed something. I want this information to be an effective teacher so I can explain it when they have a question. (Unlike when I asked in high school.)

So, I can be greatly mistaken.

Danny

#### DanoDragon

##### New member
Posted as written in the text....to be honest, I'm not even sure K & W are supposed to be a part of the first part of the problem.

Danny

#### Random

##### New member
I was going to type this before, but wasnt sure if "call" meant telephone so you would have to deal with the letters on the numbers, so here goes:

For part A:
How many possibilities are there for the first letter? (K and W)
How many letters are in the alphabet?
How many letters are in the alphabet?
How many letters are in the alphabet?
You need to multiply all these together. You need to think how many possiblities there are for each character. Since the first character has W or K for the possibility, you only have 2 possibilities. The other 3 letters could be any letter, and there are 26 letters in the alphabet, so you muliply all of these together. So, 2*26*26*26=35152
There are 35152 possible station names.

For part 2 (this is where I stopped typing before because there would only be 1 possible station!):
If KIDS is the name of the radio station... it is only one possible name so 1/35152

Very poor question, but multiplying like above removes the exponents... I think I learned this type of probability before I touched exponents.