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Math Help - Annoying permutations question

  1. #1
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    Lightbulb Annoying permutations question

    hey mathematicians, I need some help with permutations and probability

    1. How many ways can you arrange the letters in the world DEPRESSING


    a) without restriction


    This one is easy. 10!/2!x2! = 907200

    b) What is the probability that the S is the last letter?

    Can't do this one. The answer is 1/10. (NOTE: There are two S's and two E's.)

    2. How many ways can you arrange the numbers 1 2 3 4 5 6 7 8 9 so that the odd numbers appear in ascending order?

    3. A spinner is has parts A B C D E on it so that the probability of spinning on any letter is 1/5. (equally likely). Hence the probability of spinning A, B, C, D and E is 20%. How many times does the spinner have to be spun so that Michael can say that the chances of having at least one E is 99%?

    4. A dice has numbers 1 2 3 4 5 6 on it. It is biased so that the probability of rolling a 1 is 50% and equally likely to roll on the other numbers. What is the probability of rolling a six?

    I don't get this. The probability of a 1 is 50%. Does that mean the probability for each of the numbers will be (100 - 50)/5 = 10% for the other numbers. If so, then the chances of rolling a six will be 10%.
    What do you think?


    THANKS GENIUSES
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  2. #2
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    Quote Originally Posted by differentiate View Post
    1. How many ways can you arrange the letters in the world DEPRESSING
    b) What is the probability that the S is the last letter?
    Can't do this one. The answer is 1/10. (NOTE: There are two S's and two E's.)
    I disagree with the answer \frac{1}{10}.
    The correct answer is \frac{1}{5}
    There are \frac{9!}{2!} ways for the arrangement to end in S.
    So {\displaystyle{\frac{9!}{2!}}/{\frac{10!}{2!^2}}=\frac{1}{5}}.
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