Write a recurrence relation T(n) such that T(n) is the number of possible permutations of a word of length n such that all n characters are distinct. Solve the obtained recurrence relation to get a closed formula for the number of possible permutations for each word.

C++ Code: Displays all possible permutations of a word

// this function prints all the permutations of a user entered string void permutation(string word, string sstore) { // test if word was entered if (word.size() != 0) { // rotates all characters to the beginning one at a time for (int i = 0; i < word.size(); i++) { // take the first character and store it permutation(word.substr(1), sstore + word[0]); // rotate and move the second character to the beginning rotate(word.begin(), word.begin() + 1, word.end()); } } // if no word was entered else { cout << sstore << endl; return; } } // picks up user input and sends to the function int main() { string word; cout << "Enter a word: "; cin >> word; cout << endl; permutation(word, ""); return 0; }