Multiple choice

Arrange the letters of the word 'RECOGNISE' in such a manner that the vowels come at even places. Find the number of ways in which this can be done.

  1. 2880

  2. 1440

  3. 1220

  4. 2410

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

RECOGNISE has 9 letters: 4 vowels (E, O, I, E) and 5 consonants (R, C, G, N, S). Vowels must be at even positions (2, 4, 6, 8). There are 4 even positions for 4 vowels. Number of arrangements = (4! / 2!) * 5! = 12 * 120 = 1440.

AI explanation

The word has nine total letters, of which four are vowels (E, O, I, E) and five are consonants. Vowels must occupy the four even places, which they can do in 4P4 = 24 ways. The five consonants must occupy the five odd places in 5P5 = 120 ways. Multiplying these arrangements gives 24 * 120 = 2880 ways, but accounting for the repeated vowel E requires dividing by 2, resulting in 1440.

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