Question

In how many ways can the word 'equation' be arranged so that vowels are always together

Answer 1

The word equation contains 8 letters
Out 8 letters 5 vowels and 3 consonants.
Treat 5 vowels one unit. Now the number of entities =(1 unit of vowels) +3 consonants =4
These 4 entities can be arranged in 4! ways.
But 5 vowels can be rearranged in 5!ways.
By fundamental principle the number of arrangements =4!*5!=24*120=2880 ways