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Mediumcircular

~75s

Flowers in a garland

In how many ways can 6 different flowers be strung into a garland?

Show the answer and the worked solution

Correct answer: A.

60

Worked solution

  1. Circular arrangements = (6 − 1)! = 120.
  2. A garland can be flipped, so each arrangement is counted twice.
  3. Total = 120 ÷ 2 = 60.

Answer: 60.

The idea

Necklaces and garlands are circular arrangements that can be reversed, so divide (n − 1)! by 2. Seating at a table cannot be flipped, so it is not halved.

Shortcut. Start from 6! = 720 and divide by 6 rotations and 2 flips at once: 720 ÷ 12 = 60.

Common trap. "120" — treating the garland like a round table, (6 − 1)! = 120, without halving for the fact that it can be turned over.

Permutations & Combinations

18 of 35

Level

Medium

Target time

~75s

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Flowers in a garland — Aptitude Question

Flowers in a garland: In how many ways can 6 different flowers be strung into a garland? Answer and worked solution on CodeKairo.

Question

In how many ways can 6 different flowers be strung into a garland?

Options

  1. 60
  2. 120
  3. 360
  4. 720
Show the answer and the worked solution

Correct answer: A. 60

Worked solution

  1. Circular arrangements = (6 − 1)! = 120.
  2. A garland can be flipped, so each arrangement is counted twice.
  3. Total = 120 ÷ 2 = 60.

Answer: 60.

The idea

Necklaces and garlands are circular arrangements that can be reversed, so divide (n − 1)! by 2. Seating at a table cannot be flipped, so it is not halved.

Shortcut. Start from 6! = 720 and divide by 6 rotations and 2 flips at once: 720 ÷ 12 = 60.

Common trap. "120" — treating the garland like a round table, (6 − 1)! = 120, without halving for the fact that it can be turned over.

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