Multiple choice

How many words can be formed from the letters of the words ARTICLE, if vowels always come at the odd places:

  1. $60$
  2. $576$
  3. $\dfrac{{7!}}{{3!}}$
  4. $120$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

ARTICLE has 7 letters: 3 vowels (A, I, E) and 4 consonants (R, T, C, L). Odd positions are 1, 3, 5, 7 (4 spots). Vowels must be in odd positions: 4P3 = 4 * 3 * 2 = 24 ways. Remaining 4 letters in 4 spots: 4! = 24 ways. Total = 24 * 24 = 576.

AI explanation

The word ARTICLE has 7 letters, including 3 vowels (A, I, E) and 4 consonants. The 4 odd positions (1st, 3rd, 5th, and 7th) can be filled by the 3 vowels in 4P3 ways, which is 4! divided by (4-3)!, giving 24 ways. The remaining 4 even positions must be filled by the 4 distinct consonants, which can be done in 4! ways, or 24 ways. Multiplying these together gives 24 * 24 = 576 words.

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