First slide

Theorems of probability

Question

At random all the letters of the word "Article" are arranged in all possible ways. The probability that the arrangement begins with vowel and ends with a consonant is

Easy

A

$\frac{1}{7}$
B

$\frac{2}{7}$
C

$\frac{3}{7}$
D

$\frac{4}{7}$

Solution

The number of letters in the word ARTICLE is 7
Hence, the number of ways of arranging the letters among themselves without any restriction is 7!
Therefore, $n (S) = 7!$
The number of vowels is 3, and the number of consonants is 4

suppose that E be the event of getting words which starts with vowel and ends with consonants

$n (E) = 3_{C_{1}} \times 4_{C_{1}} \times 5!$
$P (E) = \frac{3 \times 4 \times 5!}{7!} = \frac{2}{7}$
The probability that the arrangement begins with vowel and ends with a consonant is $\frac{2}{7}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App