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What is the probability that if 14 letters are typed, no letters are repeated?

Round your answer to 6 decimal places as needed.

1 Answer

5 votes

Answer: 0.013051

Step-by-step explanation

We have 26 letters to pick from in the set A,B,C,...,X,Y,Z

When repeats are allowed, there are roughly 26^14 = 6.4509975 * 10¹⁹ different 14 letter "words" we can form. Scientific notation is needed because the result is a really large number. Most of these words won't be found in the dictionary as they'll be a string of nonsensical letter patterns.

If repeated letters weren't allowed, then we would have 8.4194178 * 10¹⁷ different permutations. Use the nPr formula with n = 26 and r = 14 to get that value mentioned. Or the scratch work calculation would look like this:

26*25*24*23*22*21*20*19*18*17*16*15*14*13 = 8.4194178 * 10¹⁷ approximately.

From here we divide the two values

(8.4194178 * 10¹⁷)/(6.4509975 * 10¹⁹)

= (8.4194178/6.4509975)*(10¹⁷/10¹⁹)

= 1.3051343*10¹⁷⁻¹⁹

= 1.3051343*10⁻²

= 0.013051343

= 0.013051

There's about a 1.305% chance of randomly typing out a 14 letter word that has no repeated letters.

User Vikas Roy
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