Question

The letters of the word SAVITA are arranged at random. Find the probability that vowels are always together.

Answer 1

The word SAVITA contains 6 letters. Out of 6 letters, 3 are vowels (A, A, I) and 3 are consonants (S, V, T).
6 letters in which A repeats twice can be arranged among themselves in `(6!)/(2!)` ways.

∴ n(S) = `(6!)/(2!)`
Let A be the event that vowels are always together.
3 vowels (A, A, I) can be arranged among themselves in `(3!)/(2!)` ways.
Considering 3 vowels as one group, 3 consonants and this group (i.e. altogether 4) can be arranged in ⁴P₄ = 4! ways.
∴ n(A) = `4! xx (3!)/(2!)`

∴ P(A) = `("n"("A"))/("n"("S"))`

= `(4!xx(3!)/(2!))/((6!)/(2!))`

= `(4!3!)/(6!)`

= `1/5`