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In how many different ways can the letters of the word CORPORATION be arranged so that the vowels always come together?

1. 810
2. 1440
3. 2880
4. 50400

Correct answer: 50400

Solution

CORPORATION has 11 letters: vowels O, O, A, I, O and consonants C, R, R, P, T, N. Treat the 5 vowels as one block, so we arrange 7 units: the vowel block and 6 consonants, with R repeated twice. Number of ways = 7!/2! × 5!/3! = 2520 × 20 = 50400.

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