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

Question

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

Quizplus · Accepted Answer

The number of distinguishable permutations of the group of letters G,A,U,S,S can be found using the formula for permutations with repeated elements, which is n!/ (m1!m2!...mk!) where n is the total number of elements and m1, m2, ..., mk are the number of repeated elements for each distinct element.

In this case, there are 5 elements (n=5) and 2 repetitions of the letter S (m1=2). Plugging these values into the formula, we get:

5!/ (2!1!1!1!) = 60

Therefore, there are 60 distinguishable permutations of G,A,U,S,S. The correct answer choice is D.

Find the Number of Distinguishable Permutations of the Group of Letters