problem solving

Question

If the letters of the word CALCULATED are mixed up and then randomly arranged to display a string of 10 letters, what is the probability that they will still spell CALCULATED? (Assume that no letters have been turned upside down.

Answer 1

I am not sure about this answer, but as long as no one else has tried it, I will give it a shot.  Please: if you get a better answer either here on Wyzant or elsewhere, I would appreciate knowing it.

 

The number of different arrangements of the 10 letters in CALCULATED is quite large"

10!/(2! * 2! * 2!) = 10*9*8*7*6*5*3

 

I believe the number of ways in which the letters can be arranged to spell CALCULATED is only 8:

you can choose the first letter in the first position in 2 ways, the 2nd in 2 ways and the third in 2 ways and all the rest in one way only.

 

That  makes the probability required: 1/(10*9*7*6*5*3) = 1/56700