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Find the number of arrangements of all the letters in the word 'CAT'.
A$3$
B$9$
C$27$
D$6$
Answer & Solution
Correct answer: D. $6$
1. 'CAT' has 3 DISTINCT letters: C, A, T.
2. Number of ways to arrange $n$ distinct objects in a row: $n! = 3! = 6$.
3. Enumerate: CAT, CTA, ACT, ATC, TAC, TCA — six arrangements.
4. Option A is just $n$. Option C is $n^2$. Option D is $n^n$ (would apply to selection WITH repetition).
_Source: NCERT Class 11 Mathematics, Ch 6, §6.3 + Examples, p. 5–7._
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