Permutations with 26 letters
By John Thompson
Not totally sure if I'm understanding the questions correctly:
Consider the permutations of the set of 26 letters of the English alphabet
- How many total permutations are possible? P(26,26)=26!
- How many permutations begin with a? P(26,25)
- How many permutations begin with z and end with a? P(26,24)
- How many permutations begin with the 5 vowels (in any order), which are followed by the remaining consonants (in any order)? I have no idea.
1 Answer
$\begingroup$There is only one way to put a in the first spot. Then, how many ways are there to arrange the remaining 25 letters in 25 spots? $25!$
There is only one way to put z first and 1 way to put a last. Then, how many ways are there to arrange the remaining 24 letters in 24 spots? $24!$
How many ways can we arrange the 5 vowels among five spots? $5!$ Then how many ways can we arrange the remaining 21 letters in 21 spots? $21!$ So the total ways to do this are $5!*21!$
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