Probability with Permutations Question

[lucian044]

Hello!
This is my first time posting and I would appreciate any help at all! So the problem I'm working on has to do with randomly choosing letters from the alphabet and the probabilities that they make out words. The problem reads as follows:

With your eyes closed, you are randomly selecting 4 letters from the English alphabet (made out of cube-shaped plastic blocks with one letter printed on each block) and randomly arranging them side by side on the table. When you open your eyes, what are the chances that you see the word TEAM on the table? What are the chances that you see any meaningful English word made out of the letter 'T', 'M', 'A', and 'E' on the table?

I have been trying to figure out this problem for days. I have had to solve similar problems in the past, but am really stuck on this one. I think I am having trouble with the fact that I am blindly setting the letters on the table. Any advice would be very much appreciated! Thank you!

 

[Dason]

Is this choosing with replacement? So let's say you choose your first block - does that letter get re-added for you second pick?

 

[lucian044]

No, it is not with replacement. The scenario is you choose 4 blocks all at once from the group of 26 and then place them in a row on the table

 

[Dason]

So the first is literally just asking you what is the probability that the first letter you choose is T, the second letter you choose is E (given that T was the first), the third letter is A (given that the first two were T and E), and the fourth is M (given that the first three were T, E, A).

The second is just (how many arrangements make a word)/(total # of possible arrangements of those letters).

 

[lucian044]

That makes sense, thank you so much!