Topic: Discrete Mathematics
How many four letter words can be formed using the letters of the word 'GAGANYAAN' with no repetition of letter?
- A. 3024
- B. 192
- C. 64
- D. 24
Answer: D. 24
Explanation: The word 'GAGANYAAN' contains 9 letters in total, but only 4 distinct letters: {G, A, N, Y}. We need to form a 4-letter word with NO repetition. Since there are exactly 4 distinct letters available, we must use all 4 of them (G, A, N, Y) exactly once. The number of ways to arrange 4 distinct letters is $4! = 4 \times 3 \times 2 \times 1 = 24$.