What is probability that 17 letters dumped out will land face up, in the correct order to spell two words?

Question

That discovered, what is the probability that the same letters will not only spell the words but will be within 20 degrees of the same angle?

OK, here are the letters: D, E, E, E, G, G, I, I, I, L, L, N, N, N, S, T, T. There are no other letters in the bag. These letters spell a two-word phrase.

Answer 1

this is not a simple mathematical probability only. ©

you also invoke chaos theory here. the randomness of the fall of the letters. that will mean that there is a very little chance of that occurring. (close to zero)

you need to determine whether they will form a letter. if simply arranged in a straight line without the dumping of the letters, this will be a simple probability question. another matter here is if only english words are included.

then you need to determine the chance that upon dumping the letters will form the desired formation. this is based on the initial condition of the letters from the container.

you multiply those probabilities to get the overall answer.

Answer 2

well you would first consider 3 letters in the bag say C A T, the chances of them landing in that order is 1/6 i.e:
act
atc
cta
cat
tca
tac
you can see that there will be 3! i.e. 3*2*1=6 outcomes of which 1 is the correct word cat. so chances are 17 factorial (17*16*15*14....*1).. if the letters were different. with regards to the angle im afraid thats a near impossibility, you will see pigs fly first

Answer 3

It depends on what letters are in the bag. If the contents are seventy-five copies of the letter Q, the chances of spelling a word are slim.

Answer 4

Very very very slim.