Bunuel wrote:
A new word is to be formed by randomly rearranging the letters of the word ALGEBRA. What is the probability that the new word has consonants occupying only the positions currently occupied by consonants in the word ALGEBRA?
(A) 2/120
(B) 1/24
(C) 1/6
(D) 2/105
(E) 1/35
Probability method of solving:Question requires the consonants occupying the same positions (they can interchange - a mistake I did at first). And if the consonants are at their positions, then the vowels would also need to be in their respective positions (and they can interchange as well).
There are initially 3 vowels and 4 consonants.
Hence position-wise probability = \(\frac{3}{7}*\frac{4}{6}*\frac{3}{5}*\frac{2}{4}*\frac{2}{3}*\frac{1}{2}*1 = \frac{1}{35}\)
Answer
E.
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