SOLUTION: A Discrete Mathematics student comes from the village of KILLAHOURAGAIN. As an hilarious jape, on the way home from a late-night study session, he decides to rearrange the letters

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Question 1172924: A Discrete Mathematics student comes from the village of KILLAHOURAGAIN. As an hilarious jape, on the way home from
a late-night study session, he decides to rearrange the letters on
one of the sign-posts.
How many arrangements of the letters in KILLAHOURAGAIN
are possible?
Answer:
Of these arrangements, how many have all the L’s together?
Answer:
Of these arrangements, how may have all the letters in alphabetical order?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) The name has 14 letters, including 3 of one letter and 2 each of two other letters. By a well known counting principle, the number of distinct arrangements is

14%21%2F%28%283%21%29%282%21%29%282%21%29%29

(2) To find the number of distinct arrangements with the two L's together, simply treat the two L's as a single "letter"; that gives 13 letters with 3 of one letter and 2 of another; the number of distinct arrangements is

13%21%2F%28%283%21%29%282%21%29%29

(3) There is only distinct arrangement in which all the letters are in alphabetical order.