SOLUTION: A seven-digit number (i.e. a whole number between 1000000 and 9999999) is selected at random. What is the probability that it contains no digits other than 6's, 7's, and/or 8's

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Question 1122709: A seven-digit number (i.e. a whole number between 1000000 and 9999999) is selected at random.
What is the probability that it contains no digits other than 6's, 7's, and/or 8's?

What is the probability it contains two 6's, three 7's, and two 8's?

Enter your answers as fractions in lowest terms.
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.
A seven-digit number (i.e. a whole number between 1000000 and 9999999) is selected at random. 

a)  What is the probability that it contains no digits other than 6's, 7's, and/or 8's? 
 

    It means that the given integer number is written using only the digits "6", "7" and/or "8".


    You may have any of these three digits in the 1-st (leftmost) position;
                 any of these three digits in the 2-nd            position;
                 any of these three digits in the 3-rd            position;

                 . . . . .       and so on  . . . . . . . . 

                 any of these three digits in the 7-th            position.


    In all, it gives you  3%5E7 = 2187 different numbers.


    To find the probability under the question, divide this number by 9000000,
       which is the number of all 7-digit numbers from 1000000  to  9999999.


    You will get the answer :  the probability under the question = 3%5E7%2F%289%2A10%5E6%29 = 3%5E5%2F10%5E6,

        "expressed as fractions in lowest terms".
           


b)  What is the probability it contains two 6's, three 7's, and two 8's? 
 

Enter your answers as fractions in lowest terms.