anonymous
  • anonymous
How many strings of eight uppercase English letters are there that start with X, if no letter can be repeated?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
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Mani_Jha
  • 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?
anonymous
  • anonymous
Oh okay, but shouldn't it be 25*24*...*19 instead?
Mani_Jha
  • Mani_Jha
Oh yeah, I am sorry! You're correct.

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anonymous
  • anonymous
Haha thank you, I was thrown off by that fixed X as the first letter of the string..
Mani_Jha
  • 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.
anonymous
  • anonymous
haha yeah, I was just lazy to type the whole fraction out..but thanks :D
anonymous
  • anonymous
if the string should start with the letters BO (in this order), and if letters can be repeated, will it be 26^6?
Mani_Jha
  • Mani_Jha
Yes, exactly.

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