Find the number of different 8-letter arrangements that can be made from the letters of the word EDUCATION so that all vowels occur together.(a) 40320(b) 37440(c) 1440(d) 2880I got this question in a job interview.My question is from Permutations-2 topic in chapter Permutations and Combinations of Mathematics – Class 11

Find the number of different 8-letter arrangements that can be made fr

1.	Find the number of different 8-letter arrangements that can be made from the letters of the word EDUCATION so that all vowels occur together.(a) 40320(b) 37440(c) 1440(d) 2880I got this question in a job interview.My question is from Permutations-2 topic in chapter Permutations and Combinations of Mathematics – Class 11
Answer» The correct answer is (d) 2880 Explanation: There are 5 vowels in WORD EDUCATION. 5 vowels can be arranged in ^5P5 i.e. 5! ways. When all vowels are together, 5 vowels together FORM one LETTER and remaining 3 letters i.e. together 4 letters can be arranged in ^4P4 i.e. 4! ways. Total possible arrangements are 5! * 4! = 120*24 = 2880.

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