Multiple choice

In how many different ways can the letters of the word 'GEOGRAPHY' be arranged such that the vowels must always come together?

  1. 2520

  2. 2530

  3. 15130

  4. 15120
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D Correct answer
Explanation

GEOGRAPHY has 9 letters: G, E, O, G, R, A, P, H, Y. Vowels: E, A, O (3). Consonants: G, G, R, P, H, Y (6). Treating the 3 vowels as one block, we have 7 items to arrange: (EAO), G, G, R, P, H, Y. Arrangements = 7! / 2! (for the two Gs) = 5040 / 2 = 2520. Within the block, the 3 vowels can be arranged in 3! = 6 ways. Total = 2520 * 6 = 15120.

AI explanation

The word GEOGRAPHY has 9 letters with R repeated twice. The vowels are E, O, A and Y, which when grouped together act as a single unit, giving 6 total items to arrange with R repeated twice: 6! / 2! = 360. The 4 vowels can be arranged among themselves in 4! = 24 ways. Multiplying these gives 360 * 24 = 15120 ways.

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