In how many different ways can the letters of the word ‘APPRECIATE’ be arranged so that all the vowels always come together? शब्द 'APPRECIATE' के अक्षरों को कितने विभिन्न तरीके से व्यवस्थित कर सकते है कि सभी स्वर एक साथ रहें?

The word APPRECIATE has 10 letters with A twice, P twice, and vowels A, E, A, I, E (5 vowels with A and E each repeated). Treat vowels as one block. Arrangements of 6 items (5 consonants + 1 vowel block) with P repeated twice is 6!/2! = 360. Internal arrangements of 5 vowels (A, A, E, E, I) is 5!/(2! × 2!) = 30. Total = 360 × 30 = 10800.