Question

How many 4-letter words with at least one consonant can be constructed from the letters A B C D and E? It does not have to be a word in the English language and letters may repeat.

Answer 1

Let me write what I thought.

Answer 2

I have four spaces: __ __ __ __

Answer 3

I can choose any of the letters of the alphabet on the first position, so:

Answer 4

26 __ __ __

Answer 5

Now, I can choose 5 letters (the vowels on each on the remaining spaces)

Answer 6

26*5*5*5

Answer 7

And I can do this in four different ways..

Answer 8

26*5*5*5*4

Answer 9

Why are you using the whole alphabet?

Answer 10

I know this was posted before but I could not understand it. =/

Answer 11

HINT: Whenever there is "at-least" think about using mutual-inclusion-exclusion.

Answer 12

Because you can choose any letter for the first position @across

Answer 13

Oh, I was reading the OP.

Answer 14

I was doing something like that yesterday, and I don't see the relationship. @FFM

Answer 15

What is exactly mutual-inclusion-exclusion?

Answer 16

How many 4-letter words with at least one consonant can be constructed from the letters A B C D and E?

What is the answer ?

Answer 17

My answer is 13000

Answer 18

I mean the right answer.

Answer 19

Mmm I don't know.

Answer 20

Well, calculated 609

Answer 21

But I don't understand her reasoning.

Answer 22

I believe the answer should be \(5^5 - 2^5\) using only the given letters.

Answer 23

Ok, now I have 3 different answers. I think I'll better read about what you said to me.

Answer 24

and assuming that the letters are repeating.

Answer 25

Because I'm very lost with this counting techniques

Answer 26

Yes, they can be repeated.

Answer 27

hey remeber me the one u reported yesterday snowball

Answer 28

FFM, I believe you meant to say \(5^4-2^4\) since it's a 4-letter word.\[\]