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In how many arrangements of the letters of DAUGHTER are the vowels never all together?

Competition practicePermutations & Combinations

A4320
B36000
C40320
D35280

Step-by-Step Solution

All arrangements:

8! = 40320

. Vowels A, U, E as one block: 6 units,

6! \times 3! = 4320

. Not all together:

40320 - 4320 = 36000

.

Answer: B) 36000

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