Multiple choice

Given below are two statements: A number of distinct 8-letter words are possible using the letters of the word SYLLABUS. If a word in chosen at random, then Statement I: The probability that the word contains the two S's together is 1 4 . Statement II: The probability that the word begins and ends with L is 1 28 . In the light of the above statements, choose the correct answer from the options given below.

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.

Reveal answer Fill a bubble to check yourself
A Correct answer
AI explanation

The word SYLLABUS has 8 letters with S repeated twice, so the total number of distinct words is 8! / 2! = 20160. For Statement I, treating the two S's as a single unit gives 7! total arrangements, so the probability is 7! / (8! / 2!) which equals 1/4. For Statement II, fixing L at both ends leaves 6 letters including two S's, giving 6! / 2! arrangements, so the probability is (6! / 2!) / 20160 which equals 1/28. Both calculations match the given statements, meaning both Statement I and Statement II are true.