How many words,with or without meaning can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

Asked by aruni_maiyer | 21st Oct, 2010, 02:14: PM

Expert Answer:

Dear student,
The word 'EQUATION' has 8 letters.
There are 5 vowels: a, e, i, o, u and 3 consonants : q, t, n.
Form 2 groups V(vowels) and C (consonants)
We first arrange the 2 groups.
These  2 groups can be arranged in 2! =2 ways
Now the group V has 5 elements, they can be arranged in 5! = 120 ways.
Now the group C has 3 elements, they can be arranged in 3! = 6 ways.
By fundamental theorem,
the total no of ways = 2! . 5! . 3!
                            = 2.120.6
                            = 1440 .

We hope that clarifies your query,
Team Topper Learning.

Answered by  | 21st Oct, 2010, 03:17: PM

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