Find the probability of getting vowels in the first, third and sixth p

1.	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» 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) = \(\frac{m}{n} = \frac{36}{720} = \frac{1}{20}\)

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»

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) = \(\frac{m}{n} = \frac{36}{720} = \frac{1}{20}\)

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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.

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