Multiple choice

How many 4-letter words can be formed using the letters of the word COLLEGE, if each letter has to be distinct?

  1. 30

  2. 60

  3. 90

  4. 120

  5. 240
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

COLLEGE has 7 letters: C, O, L, L, E, G, E. Distinct letters are C, O, L, E, G (5 letters). We need to form 4-letter words with distinct letters. This is 5P4 = 5 * 4 * 3 * 2 = 120.

AI explanation

The word COLLEGE consists of 6 distinct letters, which are C, O, L, E, G. Using the permutation formula for arranging a subset of distinct items, the number of 4-letter words is found by calculating 5P4. This evaluates to 5 factorial divided by 1 factorial, which equals 120, revealing that the word actually has 5 unique letters despite the options suggesting otherwise, but the mathematical result perfectly matches one of the choices.

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