Permutations and Combinations

Maths · Class 11

Simulation · Maths · Class 11

Tag the twins, then take the tags off

From the lesson Permutations with repeated objects in Permutations and Combinations. Change the values and watch what happens.

Tag the twins, then take the tags offMaths · Class 11

The idea behind it

NCERT §6.3.4

  • If some objects are alike, swapping them does not give a new arrangement, so dividing by the number of such swaps removes the repeats.
  • The number of arrangements of n objects of which p₁ are alike of one kind, p₂ alike of another kind, and so on, is n!/(p₁! p₂! … pₖ!).
  • BALLOON has 7 letters with L twice and O twice, so it has 7!/(2! × 2!) = 5040/4 = 1260 arrangements.
  • Pennants: 3 red, 2 blue and 1 green pennant in a row, same colours alike, give 6!/(3! × 2! × 1!) = 720/12 = 60 patterns.
  • SPORTS has S twice: 6!/2! = 360 arrangements. Arrangements of BALLOON that start with B: fix B and arrange A, L, L, O, O, N, giving 6!/(2! × 2!) = 180.
  • Check with labels: tag the two Ls as L₁ and L₂. Each arrangement with plain Ls matches 2! labelled ones, which is why we divide by 2!.