Question

Find the probability of getting vowels in the first, third and sixth place when all the letters of the word, ORANGE are arranged in nil possible ways.

Answer 1

Here, there are total 6 letters O, R, A, N, G, E in the word ORANGE.
And there are 3 vovels O, A, E

∴ The total number of ways of arranging these six letters,

n = ₆P⁶ = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

A = Event of getting vowels in the first, third and sixth place.

∴ The favourable outcomes for the event A are obtained as follows:

∴ m = ₃P³ × ₃P³ = 3! × 3!

= 6 × 6 = 36

Hence, P(A) = \(\frac{m}{n} = \frac{36}{720} = \frac{1}{20}\)