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Originally posted by John Anderton
Ok i have a maths problem .... Its a sum of probability .... I got the answer but probability is a bit dodgy and its so easy to make a mistake .... Can some one also try this problem

There is a dictionary containing only 5 letter words and there are only 4 letters viz. a, b, c, d, e. The 1st word is aaaaa the second is aaaab the third is aaaac and so on. Now we need to find the position of the word "adbca"

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as far as I'm understanding your question this has nothing to do with probability at all. This is pure base conversion from base 5 to base 10.

quote:

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Originally posted by John Anderton
(...) and there are only 4 letters viz. a, b, c, d, e.

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a, b, c, d, e are 5 letters... and what is "viz"?

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Originally posted by John Anderton
The answer i worked out is 216 .... can someone back up my answer

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Your own answer is also wrong.


Let me explain:

Given:
  5 letters: a b c d e
  dictionary:
    aaaaa
    aaaab
    aaaac
    aaaad
    aaaae
    aaaba
    aaabb
    aaabc
    (...)

Question: what position is "adbca" in?

Solution:

Look at the dictionary. This is just a simple count up, but instead of 10 numbers, they've used 5 letters. So replace every letter with a number: a = 0    b = 1   c = 2   d = 3   e = 4:
  aaaaa     00000
  aaaab     00001
  aaaac     00002
  aaaad     00003
  aaaae     00004
  aaaba     00010 note the "jump" from 04 to 10
  aaabb     00011
  aaabc     00012
  (...)       (...)

5 different letters numbers means this is base 5.
base 10 is what we know as our normal number system: When we come to the number after 9, we add a digit and start counting again from 0 for the least significant digit: 00 01 02 (...) 08 09 10 11 12 etc...

So, add an index to the dictionary and you'll see that you only have to convert the base 5 number to a base 10 number to know it's value aka position (first position is called position 0):

  dictionary | base 5 number | base 10 number (aka position)
  aaaaa          00000               0
  aaaab          00001               1
  aaaac          00002               2
  aaaad          00003               3
  aaaae          00004               4
  aaaba          00010               5
  aaabb          00011               6
  aaabc          00012               7
  (...)            (...)                (...)


Thus adbca = 03120

So all this to explain the simple following formula:

To calculate the equivalent base ten number:
= 0 * 5^4   +   3 * 5^3   +   1 * 5^2   +   2 * 5^1   +   0 * 5^0
= 410

This is not yet the answer! Now it is time to read the question again. They asked what position the number is in. And positions useually start at 1. To make no confusion say this also in your answer :

= 411 (with first position being 1)


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quote:

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Originally posted by Chrono
oh thakns cookie, yu are so brilliant
now help me please with this problem:



(its not hard, but i would love to see how does he manage to write the solution here )

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