Ranking of "Rank"

soln

The total number of words that can be formed using R, A, N, K are 4! i.e. 24.

Now the words that can be formed after RANK are RKAN, RKNA, RNAK, RNKA.

So RANK's "rank" is 24 -4 = 20

4x3x2x1 = 24 words in total, of which 6 start with an A, 6 start with a k and 6 with an N. There are also 6 words starting with an R. A is the first letter in the alphabet, so RAKN is the 19th word. RANK is therefore the 20th word.

if we rank the letters of the word RANK alphabetically: A = first, K = second, N = third and R = fourth.

We can form $4!=24$ words.

no. of words that starts with A = $1(3)(2)(1)=6$

no. of words that starts with K = $1(3)(2)(1)=6$

no. of words that starts with N = $1(3)(2)(1)=6$

we are finished with the $18$ positions

next word is

$RAKN$ ---> $19th$ $position$

then

$RANK$ ---> $20th$ $position$

c++ code

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#include <bits/stdc++.h>
using namespace std;

int main()
{
  string word = "RANK";
  sort(word.begin(),word.end());
  int i = 1;
  do
  {
    i++;
  }while(next_permutation(word.begin(), word.end()) && word != "RANK");
  cout << "Order: " << i++ << " " <<word << '\n';
  return 0;
}