Question

in how many ways can the letters of the word JUPITER be arranged in a straight line such that vowels always stay together​

Answer 1

$\mathtt{ \huge{\fbox{SOLUTION :}}}$

There are total 7 letters , of which 3 letters are vowels

The 3 vowels can be arranged in 3! ways i.e 6 ways

Assume 3 vowels together as a one letter

So, now , the total number of letter is 5

Thus , the number of permutations (when all vowels are occur together) = 5! × 3! = 720

Hence , in 720 ways the letters of the word JUPITER be arranged in a straight line such that vowels always stay together

Answer 2

Answer:

No. of vowels = U, I, E = 3

Considering (UIE) as one letter,

total no. of letters = 5 (J,P,T,R,(UIE))

Now,

no. of arrangements = 5! = 120

However, the letters of (UIE) can themselves be arranged in 3! ways,

therefore, total arrangements = 5! × 3! = 120 × 6 = 720