Question

Consider the letters of the word "EDUCATION"
1) how many distinct permutations are there.
ii) In how many of these with all vowels
occur together
ii) In how many of these with all vowels not
occur together.​

Answer 1

Answer : In the word 'equation', there are five vowels (a,e, i, o, u) and three consonants (q, t, n).

Since the vowels and consonants should always occur together, we have to group them and consider as two separate things, say V and C.

Now V and C can be arranged in two ways as VC or CV. In both these cases, the vowels and consonants are not separated.

Since the vowels are all distinct, they can be arranged in 5! ways.

Similarly, as the consonants are also distinct, they can be arranged in 3! ways.

Therefore, the total number of arrangements is 2*5!*3!

2*120*6 = 1440