Solve the problem using the idea of labeling.
-How many permutations are there of the letters in the word GIGGLE?
A) 4320
B) 720
C) 36
D) 120

Question

Quizplus · Accepted Answer

The word GIGGLE has 6 letters, but the letters G and I are repeated. To find the number of unique permutations, we use the formula for permutations of a multiset: $ \frac{n!}{n_1!n_2!...n_k!} $, where $ n $ is the total number of items, and $ n_1, n_2, ..., n_k $ are the counts of each of the repeated items. Here, $ n = 6 $, $ n_1 = 3 $ for G, and $ n_2 = 2 $ for I. So, the number of permutations is $ \frac{6!}{3!2!} = 120 $.

Solve the Problem Using the Idea of Labeling