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Mediumarrangements

~60s

Arranging the letters of LEADER

In how many ways can the letters of the word LEADER be arranged?

Show the answer and the worked solution

Correct answer: C.

360

Worked solution

  1. LEADER has 6 letters: L, E, A, D, E, R — with E appearing twice.
  2. Arrangements = 6!/2! = 720/2 = 360.

Answer: 360.

The idea

Divide n! by the factorial of each repeat count. Ignoring the repeated E gives 720, which is offered.

Shortcut. Place the two E's first: choose their positions in C(6,2) = 15 ways, then arrange L, A, D, R in the other four in 4! = 24 ways. 15 × 24 = 360.

Common trap. "720" — computing 6! as if the two E's were different letters; swapping them gives the same word, so every arrangement is counted twice.

Permutations & Combinations

7 of 35

Level

Medium

Target time

~60s

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Arranging the letters of LEADER — Aptitude Question

Arranging the letters of LEADER: In how many ways can the letters of the word LEADER be arranged? Answer and worked solution on CodeKairo.

Question

In how many ways can the letters of the word LEADER be arranged?

Options

  1. 120
  2. 240
  3. 360
  4. 720
Show the answer and the worked solution

Correct answer: C. 360

Worked solution

  1. LEADER has 6 letters: L, E, A, D, E, R — with E appearing twice.
  2. Arrangements = 6!/2! = 720/2 = 360.

Answer: 360.

The idea

Divide n! by the factorial of each repeat count. Ignoring the repeated E gives 720, which is offered.

Shortcut. Place the two E's first: choose their positions in C(6,2) = 15 ways, then arrange L, A, D, R in the other four in 4! = 24 ways. 15 × 24 = 360.

Common trap. "720" — computing 6! as if the two E's were different letters; swapping them gives the same word, so every arrangement is counted twice.

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