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anonymous

  • 4 years ago

Assume 3 digits are selected at random from the set (1,2,3,7,8,9) and are arranged in random order. What is the probability that the resulting 3 digit number is less than 700?

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  1. anonymous
    • 4 years ago
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    how ya doing?

  2. Directrix
    • 4 years ago
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    Fine until I saw this problem. :) Just kidding, CW.

  3. anonymous
    • 4 years ago
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    Ha i have tons of them....

  4. mathmate
    • 4 years ago
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    Find out how many different numbers you can make out of the three digits, and how many of those are less than 700. There are 6*5*4=120 ways to make a three digit number out of the 6 given digits. Out of these, if we were to make a number less than 700, the first digit must be less than 7 (three choices), the remaining digits have 5 and 4 choices for a total of 3*5*4=60 ways. So probability P(<700)=N(<700)/N(all)

  5. anonymous
    • 4 years ago
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    so is it 60/700

  6. mathmate
    • 4 years ago
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    N(all) is 6*5*4=120 ways with no restrictions.

  7. anonymous
    • 4 years ago
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    what would the probability be then?

  8. mathmate
    • 4 years ago
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    So probability P(<700)=N(<700)/N(all)

  9. anonymous
    • 4 years ago
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    im still not sure how this answer is supposed to look

  10. anonymous
    • 4 years ago
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    Any clues directrix?

  11. mathmate
    • 4 years ago
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    There are 60 (desirable) ways to make 3-digit numbers less than 700 out of 120 (possible) ways to make 3-digit numbers out of the given 6 distinct digits. So the probability required, P(<700) is given by P(<700) = number of desirable events / number of possible events.

  12. anonymous
    • 4 years ago
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    1/2

  13. Directrix
    • 4 years ago
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    We are making 3-digit numbers that are less than 700. So, the first digit of the 3-digit number cannot be 7, 8, or 9. For the first digit, we have 3 choices (1,2, or 3). After selecting one of (1,2,3) for the first digit, there are 5 choices left for the number's second digit, and then 4 choices for the third digit. By the Fundamental Principle of Counting, there are 3 times 5 times 4 = 60 ways to make a 3-digit number less than 700 from the given digits. 60 is the desired number of outcomes. For the probability denominator, we need the number of possible outcomes of the formation of the 3-digit number. That would be 6 times 5 times 4 or 120. The probability of creating a 3-digit number less than 700 from the digits 1,2,3,7,8,9 is 60/120 or 1/2.

  14. Directrix
    • 4 years ago
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    Sorry, CW, I had to stop eat, and then the server threw me off. I'm back now.

  15. Directrix
    • 4 years ago
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    CW, did you see my work here? Do you agree?

  16. mathmate
    • 4 years ago
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    @cw Yes, 1/2 is correct. Directrix explained everything in detail. Hope you will benefit from his excellent efforts.

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