Combinatorics

Variations with Repetition

V'(n,k) = n^k

  • High school
  • about 3 min
  • 9 of 11 in the family
Not started

Each of 2 positions has 3 choices (repetition allowed):

ABC
3pos 1
×
ABC
3pos 2
= 9

All 9 variations:

AA
AB
AC
BA
BB
BC
CA
CB
CC
V′(3,2)=32=9V'(3,2) = 3^{2} = 9
3×3⏟2×=9\underbrace{3 \times 3}_{2\times} = 9

Each of 2 positions has 3 choices (repeats allowed). Total: 3^2 = 9.

Where it is taught