## windsylph 3 years ago How many strings of eight uppercase English letters are there that start with X, if no letter can be repeated?

1. Mani_Jha

_ _ _ _ _ _ _ _ Consider the eight spaces above to be filled by eight letters. The first place can be filled in only 1 way(X) The second place can be filled in any 25 ways(any of the remaining 25 letters) The third place an be filled in any 24 ways(any of the remaining 24 letters) .......... Similarly, the total no of ways is 25X24X23..X1 =(25)! Clear?

2. windsylph

Oh okay, but shouldn't it be 25*24*...*19 instead?

3. Mani_Jha

Oh yeah, I am sorry! You're correct.

4. windsylph

Haha thank you, I was thrown off by that fixed X as the first letter of the string..

5. Mani_Jha

If you know the formula for permutations, there's a more direct way of doing this: The first letter is fixed,so now you've to choose 7 other letters from 25 letters(since X can't be used again) So, no of ways will be 25P7 Both will give you the same answer.

6. windsylph

haha yeah, I was just lazy to type the whole fraction out..but thanks :D

7. windsylph

if the string should start with the letters BO (in this order), and if letters can be repeated, will it be 26^6?

8. Mani_Jha

Yes, exactly.