How do you do permutations with repeating symbols?

Answer 1

Suppose you have n objects and within those, there arem1 objects of kind 1

m2 objects of kind 2

and so on.

Then the number of permutations of the n objects is n!/[m1!* m2!...]

For example, permutations of the word "banana"

n = 6

there are 3 "a"s so m1 = 3

there are 2 "n"s so m2 = 2

therefore, the number of permutations = 6!/(3!*2!) = 720/(3*2) = 120.