RAS question
How many different arrangements can be made using all letters of the word 'EXAM'?
Correct answer: (D) 24.
Using all four distinct letters of the word EXAM, the number of different arrangements is 4!, which equals 24.
Explanation
The word EXAM has four letters, and none of them is repeated. NCERT defines a permutation as an arrangement in a definite order; here, every arrangement uses all four available letters, so the order of E, X, A and M matters. For distinct objects taken all at a time, the count is the product of the available choices at each position: 4 choices for the first place, then 3, then 2, then 1. That product is 4! = 4 x 3 x 2 x 1 = 24. The note about repeated letters is important only when some letters are identical, because then identical swaps would be counted more than once and must be divided out.
Why the other options are wrong
- (A) 16 treats the count like 4 x 4, but each letter can be used only once when all letters of EXAM are arranged.
- (B) 12 is 4 x 3, which counts only the first two ordered positions and leaves the remaining two letters unarranged.
- (C) 48 is larger than 4! and would overcount arrangements because EXAM has only four distinct letters used once each.
Concept
This tests basic permutations of distinct objects taken all at a time. RAS reasoning questions use this idea often because it checks whether candidates can translate a word-arrangement problem into factorial counting.