Guessing alphabet letters with order

  • Thread starter Cylab
  • Start date
  • #1
We need to guess 5 letter among alphabet of A~Z. What is probability of correctly guessing 2, 3, 5 letters respectively. given they are all upper letters and alphabetic order is preserved (no Z comes before any letter, or no A comes after any letter etc).

I know mentioned it before, but I really appreciate providing any way of solving the problem. I really need to solve the problem.. please help!
Thanks in advance for you thoughts shared.
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  • #2
You need to show your efforts before we can help. What ideas have you thought of so far?

Start wit the simplest case. What is the probability of guessing 1 letter correctly?
  • #3
Thanks for your attention.
1st, Sample space: there are 26 letters and each of them can be filled up and thus sample space is 26*26*26*26*26=26^5.
2nd, let`s restrict that first letter (FL) must be one of 'A~V' (the order of 5 correct letters is same as the order of 'A~Z'), thus P(FL)=1/21. Second letter(SL) would be, if FL is 'A', is one of 'B~W', thus P(SL)=1/21 as well. But if FL is 'C', SL is one of 'C~W', thus P(SL)=1/20 . Once FL is 'D','E','F'... , then P(SL)=1/19,1/18,1/17 respectively...Thus, P(SL)=1/21+1/20... Third Letter is...This is long calculation, but I was wondering if there is any alternative way doing that...
Please feel free to offer your suggentions.
Thanks again for sharing ideas!

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