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Math Help - Question on probability

  1. #1
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    Question on probability

    Hi, I have a question on probability here,

    Five letters are chosen from the word "singapura", find the probability that the letters chosen can be used to form the word "singa".

    is it 2/(9C5) = 1/63?

    Is it possible to solve this question without using combination (nCr)?
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  2. #2
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    Hello, acc100jt!

    Five letters are chosen from the word SINGAPURA.
    Find the probability that the letters chosen can be used to form the word SINGA.

    is it: . \frac{2}{_9C_5} \:=\:\frac{1}{63} ? . . . . Yes!
    Is it possible to solve this question without using combination (nCr)?
    It is possible, but it takes more work . . .


    (1) We can list the 126 possible 5-letter samples
    . . . and then count the number that contain S,I,N,G,A (there are two).


    (2) We could work out the probability like this.

    Find the probability of getting S-I-N-G-A (in that order).

    \text{We have: }\;\underbrace{\frac{1}{9}}_S \cdot\underbrace{\frac{1}{8}}_I \cdot\underbrace{\frac{1}{7}}_N \cdot\underbrace{\frac{1}{6}}_G\cdot\underbrace{\f  rac{2}{5}}_A \;=\;\frac{1}{7560}

    Since the order is unimportant, the probability is: . 5! \times\frac{1}{7560} \;=\;\frac{1}{63}


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  3. #3
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    Yes, you can.

    (1/9)(1/8)(1/7)(1/6)(2/5)=1/7560

    But they can be arranged in 5!=120 ways, so

    120(1/7560)=\frac{1}{63}
    Last edited by galactus; August 19th 2008 at 08:29 AM. Reason: Soroban beat me to the punch. Oh well, at least we are in sync.
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