Does any letter in our group occur more than once?
420
We want to find the number of distinguishable permutations of the group of letters.
S, E, A, B, E,E, S
First, let's split the letters into groups that contain the same letter.
cc
S, S & E, E, E
B & A
The letters are divided into four groups. Let's count the letters in each group.
Letter
Number of Copies of the Letter
S
n_1= 2
E
n_2= 3
B
n_3= 1
A
n_4= 1
When we want to find the number of distinguishable permutations of a set with n elements, in which there are n_1 elements of one kind, n_2 of a second, and so on with n = n_1+...+n_k, we can use the formula for permutations with repetitions.
n!/n_1!* n_2!* ... * n_k!
In our case n = 7, n_1 = 2, n_2 = 3, n_3 = 1, and n_4= 1. Let's substitute these values into the formula for the number of distinguishable permutations of our set!
