Question

How many different words can be formed by arranging the letters of words assassination such that 'no two vowels are together'?

Answer 1

The word ASSASSINATION has 4S,3A,2I,2N,T,O,4S are together.

This is considered as one block as 1 letter

Now we have 3A,2I,2N,4S,T,O

⇒10!3!2!2!=10×9×8×7×6×5×4×3×2×1(3×2×1)×(2×1)×(2×1)

⇒10×9×8×7×5×3×2

⇒151200