How Many Words?
This problem is from Matt Compton, University of Oklahoma.
How many five-letter strings can be formed using the 26 (upper case) letters of the alphabet, subject only to the restriction that consonants cannot be next to each other and likewise vowels cannot be side by side? Assume that Y is not a vowel. A string is an ordered list in which repetition is allowed.
Submit your answers to mathpotw@acu.edu. Details for submissions can be found here.
Solution to How Many Words?
Correct solutions submitted by: Wyatt Witemeyer, Bethany Witemeyer
There are two cases to consider:
- If the five-letter string begins with a consonant, then there are (21)(5)(21)(5)(21) such strings.
- If the five-letter string begins with a vowel, then there are (5)(21)(5)(21)(5) such strings.
Hence there are (213)(52) + (212)(53) =286,650 possible such strings.
