Interesting probability question on Mathcounts

Thanks guest.  You are totally correct.

I failed to recognise that all the even numbers have a factor of 2  

I'll start again

4 numbers are randomly selected from the subset (1,2,3,4,5,6,7,8,9) . What is the probability that the product of the 4 randomly selected integers is a multiple of 14?

One of the numbers has to be 7.  AND at least one has to be even.

Forget about the 7 and there are 4 even and 4 odd numbers from which to choose the other numbers

3 evens                                  4C3                       = 4

2 evens and an odd                4C2*4C1 = 6*4   = 24

1 even and 2 odds                 4C1* 4C2 = 4*6   = 24

  Total  4+24+24 = 52               (just like guest said)

Prob = 52 / 4C9 =  52 / 126

Now we are in agreement.

Thanks Guest and Melody!!

I put 4/81 because there was \(9^4\) ways to choose the 4 numbers

I thought there was only 4 x 1 x 9 x 9 options, because 1 has to be 7, 1 has to be of the 4 even numbers listed in the subset, and the remaining 2 don't matter.

I think I accidentally accounted for order

Thank's again both Melody and Guest!!! 

You have made 2 mian logic errors here.

1) You have said that all the numbers can be used more than once, which they can't.

2) You also said that order chosen counts, you already understand that you made that mistake.  

Learning is a journey :)