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# Math with Letters

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The letters in the word TRIANGLE are arranged in all possible values and these arrangements are listed in the alphabetical order the word INTEGRAL appears in the list in which position number?

Guest Apr 9, 2017
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The letters in the word TRIANGLE are arranged in all possible values and these arrangements are listed in the alphabetical order the word INTEGRAL appears in the list in which position number?

There are 8 different letters in triangle so there are  8! ways of sorting them.

8! = 40320      Mmm that is a lot :)

TRIANGLE

in alphabet order these letters are

 T R I A N G L E A E G I L N R T I A E G L N R T I N A E G L R T I N T A E G L R I N T E A G L R I N T E G A L R I N T E G R A L

Any combination starting with A,E of G will come earlier

that is   3*7! combiations.

3*7! = 15120

Now I will look at the combinations beginning with I

If the second letter is A,E,G or L then that 'word' combination will come first.  There are 4 of these letters.

4*6! = 2880

So now we have the first 2 letters  IN.....

How many combinations do not have T as the next letter.

5*5! = 600

So now we have the first 3 letters INT

The next letter cannot be A that is

4! = 24

The next letter cannot be A that is

3! = 6

Thr third last one cannot be A or L

2*2! = 4

That is it I think

15120+2880+600+24+6+4 = 18634

So there are 18634 combinations before

So I guess that makes Integral the

18 635'th out of  40 320 possible  combinations

That is assuming that i have not made a silly mistake :)

Triangle to Integral

Melody  Apr 9, 2017

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