MHT CET · Maths · Probability
The letters of the word ' LOGARITHM' are arranged at random. The probability that arrangements starts with vowel and end with consonant is
- A \(\frac{71}{9 !}\)
- B \(\frac{18}{9 !}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{9}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\((C)\)
The word LOGARITHM contains 3 vowels and 6 consonants.
Starting vowel can be chosen from 3 vowels in 3 distinct ways and the end consonant could be chosen from 6 consonants in 6 distinct ways and the rest of 7 letters can be permuted among themselves in \(7 !\) ways.
So total number of ways this arrangement could be done are \(3 \times 6 \times 7 !\).
So, the probability that words could start with vowel and end with consonant \(=\frac{3 \times 6 \times 7 !}{9 !}=\frac{1}{4}\)
The word LOGARITHM contains 3 vowels and 6 consonants.
Starting vowel can be chosen from 3 vowels in 3 distinct ways and the end consonant could be chosen from 6 consonants in 6 distinct ways and the rest of 7 letters can be permuted among themselves in \(7 !\) ways.
So total number of ways this arrangement could be done are \(3 \times 6 \times 7 !\).
So, the probability that words could start with vowel and end with consonant \(=\frac{3 \times 6 \times 7 !}{9 !}=\frac{1}{4}\)
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