Question 1209361
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Consider four-digit numbers of the form ABCD where A,B,C,D represent digits chosen from {3,5,7,8,9} with no repeats allowed. 
The choices for A could be 7, 8 or 9 to ensure that the number exceeds 7000.
So we have 3 choices for slot A.
Whatever is selected for A, we have 4 choices for B, 3 for C, and 2 for D.
It yields 3*4*3*2 = 72 different ways to create the four-digit numbers.


Now consider the five-digit case. Numbers will look like ABCDE
Where A through E are chosen from {3,5,7,8,9} and no repeats are allowed. 
There are 5*4*3*2*1 = 120 possible five-digit values larger than 7000. 
Any permutation of these 5 digits will be larger than 7000 simply because any five-digit number is larger than any four-digit number.
We cannot form six-digit numbers or larger since we only have 5 digits to work with and repeats aren't allowed.


We found there are 72 ways to form the four-digit numbers, and 120 ways to form the five-digit numbers, such that whatever formed is larger than 7000.


Therefore,
72+120 = <font color=red>192</font> is the final answer.
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