UPCAT Mathematics practice question 37: How many distinguishable arrangements can be made from the letters of the word LEVEL?
Correct answer
A. 30
There are 5 letters with L repeated twice and E repeated twice, so the count is 5! ÷ (2! × 2!) = 120 ÷ 4 = 30.
The question
How many distinguishable arrangements can be made from the letters of the word LEVEL?
- Option A: 30Correct
- Option B: 20
- Option C: 60
- Option D: 120
Why A is correct
There are 5 letters with L repeated twice and E repeated twice, so the count is 5! ÷ (2! × 2!) = 120 ÷ 4 = 30.
Why the other options are wrong
- B 20
- Divides 5! by 6 rather than by 2! × 2!.
- C 60
- Divides by only one of the two repeated pairs, correcting for the two Ls but not the two Es.
- D 120
- This is 5! with no correction at all, so it counts identical arrangements as distinct.