Combinatorics

Permutations with Repetition

n!/(k1! × k2!)

  • High school
  • about 4 min
  • 7 of 11 in the family
Not started

Arrangements of the multiset {A,A,B} - identical letters are indistinguishable:

AA
2× A
B
1× B
→ 3

All 3 distinct arrangements:

AAB
ABA
BAA
P′(2,1)=3!2!⋅1!=3P'(2,1) = \frac{3!}{2! \cdot 1!} = 3

Out of 3! orderings many look identical because repeated letters can't be told apart. Each group of swaps counts once - hence we divide by 2!·1!.

Where it is taught