A machine randomly generates 1 of  9 numbers, 1...9, with equal likelihood. What is the probability that when John uses this machine to generate four numbers their product is divisible by 14? Express your answer as a common fract

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A machine randomly generates 1 of  9 numbers, 1...9, with equal likelihood. What is the probability that when John uses this machine to generate four numbers their product is divisible by 14? Express your answer as a common fract

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It looks like we lost. If you know someone else I can contact, please help.  The problem is burning me 

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I am wondering if we got all the numbers in the numerator. Could there be other numbers. I am thinking multiples of 14 like 14 times 4. 

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Thanks for the help. I am concerned that we are not getting all the possibilities in the denominator. Should it be 9x9x9x9. And the numerator should be 1x1x9x9. I am worried that I am not getting enough numbers in the numerator?

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