Question

In how many different ways can the letters of the word SOFTWARE be arranged in such a way that the vowels always come together?

• A. 13440
• B. 1440
• C. 360
• D. 120
• E. None of these

Answer 1

The correct option is E None of these

There are 8 letters in the word 'SOFTWARE' including 3 vowels (O, A, E) and 5 consonants (S, F, T, W, R).
Considering three vowels as one letter, we have six letters which can be arranged in ${}^6{P}_6$ = 6! ways.
But corresponding to each way of these arrangements, the vowels can be put together in 3! ways.
$\therefore$ Number of arrangements = 6! $\times$ 3
$=6\times 5\times 4\times 3\times 2\times 1\times 3\times 2\times 1$
= 4320