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How many positive integers greater than 3000000 can be formed by arranging the seven digits 1,2,2,3,6,6,6 in some order?

A number big as 3mil would be very hard to list out 

 Aug 15, 2022
 #1
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The only constraint is that the leading digit must be a 3 or greater. 

 

Can you take it from here?

 Aug 15, 2022
 #2
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1,2,2,3,6,6,6 ==7 digits

 

7! / [3!*2!] == 420 permutations

 

Each of the above 420 permutations begins with one the 7 digits this many ways:

 

420 / 7 ==60 permutations begin with 1, 2, 1 each

 

60  x  3 ==180 permutations that are less than 3,000,000

 

THerefore: 420 - 180 ==240 permutations that are > 3,000,0000

 Aug 15, 2022

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