In how many ways can the letters of the word SANFOUNDRY be rearranged such that the vowels always appear together?(a) \(\frac{(8 + 3)!}{2!}\)(b) \(\frac{6!}{2!}\)(c) 8!*3!(d) \(\frac{4!}{8!}\)This question was addressed to me during a job interview.This intriguing question comes from Counting topic in portion Counting of Discrete Mathematics

In how many ways can the letters of the word SANFOUNDRY be rearranged

1.	In how many ways can the letters of the word SANFOUNDRY be rearranged such that the vowels always appear together?(a) \(\frac{(8 + 3)!}{2!}\)(b) \(\frac{6!}{2!}\)(c) 8!*3!(d) \(\frac{4!}{8!}\)This question was addressed to me during a job interview.This intriguing question comes from Counting topic in portion Counting of Discrete Mathematics
Answer» RIGHT option is (c) 8!3! Best explanation: Take AOU together and treat it LIKE 1 entity and arrange SNFNDRY in 8! Ways. Then, the AOU can be arranged in 3! ways. So, TOTAL arrangements = 8! 3! = 40320 * 6 = 241920.

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