Question

The letters of word PROMISE are arranged so that no two of the vowels should come together. Find the total number of arrangements.

• A. 49
• B. 1440
• C. 7
• D. 1898

Answer 1

The correct option is B 1440

The four consonants can be written in 4! ways i.e., 24 ways, The three vowels can be written in 3! ways. i.e, 6 ways. Since no two vowels can come together therefore vowels can be inserted in any three places out of the five places available, such as

$i.e,in{}^5{C}_{3}waysi.e.,10ways$

Total number of arrangements required

$=24\times 6\times 10=1440$