Does any letter in our group occur more than once?
302 400
We want to find the number of distinguishable permutations of the group of letters.
B, O, B, B, L,E, H, E, A, D
First, let's split the letters into groups that contain the same letter.
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B, B, B & & O
L & & E, E
A & D & H
The letters are divided into seven groups. Let's count the letters in each group.
Letter
Number of Copies of the Letter
B
n_1= 3
O
n_2= 1
L
n_3= 1
E
n_4= 2
A
n_5 = 1
D
n_6 = 1
H
n_7 = 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 = 10, n_1 = 3, n_2 = 1, n_3 = 1, n_4= 2, n_5 = 1, n_6 = 1, and n_7= 1. Let's substitute these values into the formula for the number of distinguishable permutations of our set!
