Maths · Permutations and combinations
At random all the letters of the word "ARTICLE" are arranged in all possible way
At random all the letters of the word "ARTICLE" are arranged in all possible ways. The probability that the arrangement begins with vowel and ends with a consonant is
- A. \( 1 / 7 \)
- B. \( 2 / 7 \)
- C. \( 3 / 7 \)
- D. \( 4 / 7 \)
Step-by-step solution
Total arrangements of 7 distinct letters = 7! = 5040. For arrangements beginning with a vowel and ending with a consonant: choose first letter from 3 vowels (3 ways), last letter from 4 consonants (4 ways), arrange remaining 5 letters in 5! = 120 ways. Favorable = 3×4×120 = 1440. Probability = 1440/5040 = 2/7.