ABIILLNRT
There are
distinct ways to arrange the letters of the word “BRILLIANT.” Suppose we sort all these arrangements in alphabetical order. What is the last letter of the 20,170th arrangement?
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1 solution
The number of permutations that begin with A is 2 ! 2 ! 8 ! . The number of permutations that start with B is also 2 ! 2 ! 8 ! . Adding these numbers together results in 20,160. So we need to find the 10th permutation (going in alphabetical order) that starts with I. The first 6 are accounted for by permuting the last three letters N, R, and T. So, the next 4 has L as the third to last, and N as the fourth to last. These are LRT, LTR, RLT, and, finally, RTL.