In how many different ways can be letters of the word SOFTWARE be arranged in such a way that the vowels always come together?
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There are 8 letters in the word software of which 3 are vowels (o,a and e). Let us bunch up the 3 vowels together and treat them as one letter. So, there are now 6 letters [ s,f,t,w,r & (oae)]. Now, the 6 letters can be arranged in 6! = 720 ways and the 3 vowels can be arranged among themselves in 3! = 6 ways. Hence, required number of arrangements of the letters in software so that the vowels are always together is 720 x 6 = 4320.
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There are 8 letters in the word software of which 3 are vowels (o,a and e). Let us bunch up the 3 vowels together and treat them as one letter. So, there are now 6 letters [ s,f,t,w,r & (oae)]. Now, the 6 letters can be arranged in 6! = 720 ways and the 3 vowels can be arranged among themselves in 3! = 6 ways. Hence, required number of arrangements of the letters in software so that the vowels are always together is 720 x 6 = 4320.
HOPE IT HELPS YOU
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