Find the number of distinguishable permutations of the group of letters.
$$\mathrm { G } , \mathrm { A } , \mathrm { U } , \mathrm { S } , \mathrm { S }$$
A) 60
B) 120
C) 30
D) 5
E) 15

Question

Quizplus · Accepted Answer

The total number of distinguishable permutations of the letters in "GAUSS" can be calculated using the formula for permutations of a multiset: $\frac{n!}{n_1!n_2!...n_k!}$, where $n$ is the total number of items to be arranged, and $n_1, n_2, ..., n_k$ are the counts of each distinct item. Here, we have a total of 5 letters with the letter "S" repeating twice. Thus, the formula gives us $\frac{5!}{2!} = 120$, indicating 120 distinguishable permutations.

Find the Number of Distinguishable Permutations of the Group of Letters