anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
how ya doing?
Directrix
  • Directrix
Fine until I saw this problem. :) Just kidding, CW.
anonymous
  • anonymous
Ha i have tons of them....

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mathmate
  • mathmate
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)
anonymous
  • anonymous
so is it 60/700
mathmate
  • mathmate
N(all) is 6*5*4=120 ways with no restrictions.
anonymous
  • anonymous
what would the probability be then?
mathmate
  • mathmate
So probability P(<700)=N(<700)/N(all)
anonymous
  • anonymous
im still not sure how this answer is supposed to look
anonymous
  • anonymous
Any clues directrix?
mathmate
  • mathmate
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.
anonymous
  • anonymous
1/2
Directrix
  • Directrix
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.
Directrix
  • Directrix
Sorry, CW, I had to stop eat, and then the server threw me off. I'm back now.
Directrix
  • Directrix
CW, did you see my work here? Do you agree?
mathmate
  • mathmate
@cw Yes, 1/2 is correct. Directrix explained everything in detail. Hope you will benefit from his excellent efforts.

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