How many seven-letter words contain at least one X?

How many seven-letter words contain at least two X's?

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- January 11th 2010, 01:04 PMkturfMore Fundamental Counting
How many seven-letter words contain at least one X?

How many seven-letter words contain at least two X's? - January 11th 2010, 02:53 PMDrexel28
- January 12th 2010, 06:16 AMkturfHere's what I think...
At least one X:

26!/6!(26-6)! + 25!/(25-5)! + .... 22!/(22-2)! + 1

At least 2 X's would begin at 25...

Is that right? Or is it something to do with 26^7 minus something? - January 12th 2010, 07:23 AMPlato
- January 12th 2010, 07:25 AMkturf
So would it be 25^6 that contain 1 X and 25^5 that contain 2 X's?

- January 12th 2010, 07:39 AMPlato
- January 12th 2010, 08:43 AMkturf
For a word with 7 letters and exactly one X, the answer is 7 times 25^6 because you have seven spots available and 25 other possible letters for the 6 spots that are not the X.

So, for one or more X's, the answer would be

7 times 25^6 + 7 times 25^5 + 7 times 25^4 + 7 times 25^3 + 7 times 25^2 + 7 times 25 + 1? - January 12th 2010, 09:07 AMPlato
- January 12th 2010, 09:44 AMkturf
If you could explain why, that would be very helpful.

- January 12th 2010, 10:27 AMPlato