How many ways can the letters in illini be arranged?

Answer 1

The word "illini" consists of 6 letters, where 'i' appears 3 times, 'l' appears 2 times, and 'n' appears 1 time. To find the number of distinct arrangements, we use the formula for permutations of multiset: ( \frac{n!}{n_1! \times n_2! \times n_3!} ), where ( n ) is the total number of letters and ( n_1, n_2, n_3 ) are the frequencies of each distinct letter. This gives us ( \frac{6!}{3! \times 2! \times 1!} = \frac{720}{6 \times 2 \times 1} = 60 ). Therefore, there are 60 distinct arrangements of the letters in "illini."