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

#1**+1 **

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