# Solve the following: The letters of the word 'EQUATION' are arranged in a row. Find the probability that Arrangement starts with a vowel and ends with a consonant - Mathematics and Statistics

Sum

Solve the following:

The letters of the word 'EQUATION' are arranged in a row. Find the probability that Arrangement starts with a vowel and ends with a consonant

#### Solution

The word EQUATION has 8 letters of which 5 (A, E, I, O, U) are vowels and 3 (Q, T, N) consonants.

The 8 letters can be arranged in 8! ways

∴ n(S) = 8!

Let B ≡ the event that arrangement starts with a vowel and ends with a consonant.

Since there are 5 vowels and 3 consonants, the first place can be arranged in 5 ways and last place can be arranged in 3 ways

After this the remaining 6 places can be arranged from remaining 6 letters in 6P6 = 6! ways.

∴ n(B) = 5 x 3 x 6!

∴ P(B) = ("n"("B"))/("n"("S"))

= (5 xx 3 xx6!)/(8!)

= (5 xx 3 xx 6!)/(8 xx 7 xx 6!)

= 15/56

Concept: Basic Terminologies
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 9 Probability
Miscellaneous Exercise 9 | Q II. (1) (b) | Page 213