SOLUTION: Of the seven-letter words that can be formed without repetition from the letters of the word INCLUDE how many have the letters N and D separated by more than two letters?

Algebra ->  Permutations -> SOLUTION: Of the seven-letter words that can be formed without repetition from the letters of the word INCLUDE how many have the letters N and D separated by more than two letters?      Log On


   

Question 1149532: Of the seven-letter words that can be formed without repetition from the letters of the word INCLUDE
how many have the letters N and D separated by more than two letters?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


I will assume this question is from the same student that asked the number of words when the letters N and D are separated by EXACTLY two letters....

Then, continuing in the same manner as in my response to that question....

(1) N and D separated by THREE letters: (3)(2)(120) = 720
(2) N and D separated by FOUR letters: (2)(2)(120) = 480
(3) N and D separated by FIVE letters (the maximum): (1)(2)(120) = 240

ANSWER: 1440

Notice we can see that this method of counting the numbers of words with different numbers of letters between N and D is valid by finding the numbers of words for ALL the possible distances between N and D and showing that the sum is 7! =5040.

N and D separated by ONE letter: (5)(2)(120) = 1200
N and D separated by ZERO letters: (6)(2)(120) = 1440

That, together with the above response for this question and the earlier response for the case with 2 letters between N and D, gives us:
0 letters between: 1440
1 letter between:  1200
2 letters between:  960
3 letters between:  720
4 letters between:  480
5 letters between:  240
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           total   5040