Combinatorics: factorials, permutations (Janice creates alphabetical list containing all arrangements of letters in FELINES)

[winny]

Janice creates an alphabetical list (based on the English alphabet) containing all the arrangements of the letters in the word FELINES. Word 1 on her list is EEFILNS. What number is the word NIEELFS?

Answer is word 1983.

Please give me each steps for solving. This is for 7th and 8th class students. They want shortcut math steps on how to derive 1983 quickly. Thank you for your help and time.

 

[Dr.Peterson]

Janice creates an alphabetical list (based on the English alphabet) containing all the arrangements of the letters in the word FELINES. Word 1 on her list is EEFILNS. What number is the word NIEELFS?

Answer is word 1983.

Please give me each steps for solving. This is for 7th and 8th class students. They want shortcut math steps on how to derive 1983 quickly. Thank you for your help and time.

Do you have any thoughts of your own? Where did the question come from? What has this class learned that might be relevant? Are they themselves willing to think hard about it?

If you want an answer without having to think for yourselves and grow in your problem-solving abilities, search for "rank of a permutation" or "[dictionary] rank of a word".