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

Jasonkiln Aug 15, 2022

#1**0 **

The only constraint is that the leading digit must be a 3 or greater.

Can you take it from here?

BuilderBoi Aug 15, 2022

#2**0 **

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**

Guest Aug 15, 2022