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How many arrangements of the letters of the word 'DAUGHTER' have no two vowels next to each other?

Competition practiceProbability & Permutation

A36,000
B4,320
C14,400
D7,200

Step-by-Step Solution

Arrange the 5 consonants:

5! = 120

. They leave 6 gaps; place A, U, E in 3 of them:

^{6} P_{3} = 120

. Total

120 \times 120 = 14400

.

Answer: C) 14,400

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