All the 720 arrangements of the digits 1 through 6 are put in numerical order. What is the 248th term?

Guest Oct 14, 2020

#1**0 **

The 6 numbers 1 to 6 have: 6! =720 permutations . Each permutation begins with one of the 6 numbers this many times: 720 / 6 =120 times with each number. So, the first 120 permutations will begin with 1. The next 120 permutations will begin with 2. So, that is: 120 + 120 =240 permutations. The next 120 will begin with 3 as follows: 312456 , 312465 , 312546 , 312564 , 312645 , 312654 , 314256 ,** 314265**.......etc. So, the 8th permutation beginning with 3 =**314265**, and that is the 240 + 8 =**248th permutation.**

Guest Oct 14, 2020