How many distinct 5-letter code words can be formed from the letters in the word "TANTE" if the letters may not be repeated?

Alright Igimoh — let's do this. First, let's analyze the letters in the word "TANTE": T, A, N, T, E. There are 5 letters in total. The distinct letters are T, A, N, E. There are 4 distinct letters. i) The letters may not be repeated? Step 1: Identify the total number of letters and any repetitions. The word "TANTE" has 5 letters. The letter 'T' appears twice, while 'A', 'N', and 'E' appear once. We are forming a 5-letter code word using these 5 letters, and the letters may not be repeated (meaning each instance of a letter is used exactly once). This is a permutation of a multiset. Step 2: Apply the formula for permutations with repeated items. The number of distinct permutations of n objects where there are n_1 identical objects of type 1, n_2 identical objects of type 2, etc., is given by (n!)/(n_1! n_2! ...). Here, n=5 (total letters). The letter '