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
ISRO CS 2025 Q.62: solution and answer
Answer and solution
ANSWER
The number of four-letter words with no repeated letter is , option (d).
Official answer: DSource: ISRO's final answer key of 15 May 2026
Count the letters of GAGANYAAN (9 letters in all): G appears 2 times, A appears 4 times, N appears 2 times and Y appears 1 time.
The set of distinct letters is , which has exactly 4 members.
"No repetition of letter" means no letter may appear twice in the word. A four-letter word therefore needs 4 different letters, and only 4 different letters exist, so every word must use G, A, N and Y exactly once each.
The number of such words is the number of arrangements of 4 distinct letters: .
Option (a), , would be the count if all 9 letters were different, which they are not. Hence the answer is .
KEY IDEA
With no repetition allowed, only the distinct letters matter. GAGANYAAN has just 4 distinct letters (G, A, N, Y), so each word uses all four once, giving arrangements.
WATCH OUT FOR
Treating the 9 letters as all different and computing , or using the repeated-letter formula . Repeated copies of a letter do not give extra words when a letter may be used at most once.
From the ISRO CS 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 5 ISRO Counting & axioms questions, with notes