Question

Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement starting with vowel and end with a consonent​

Answer 1

Answer:

Total words possible = 6! = 720

Vowels = O , E (2)

Consonants = M , T , H , R (4)

So total such number that start with vowel and end with consonant = 2 × 4 × 4! = 144

So probability

$= \frac{144}{720} = \frac{1}{5}$

Answer 2

Answer:

4/15

Step-by-step explanation:

n(S)=6! Since the number of letters in word MOTHER is 6

Let A be the event of getting a word starting with vowel and ending with consonant

There will be 1 out of 2 vowels (for start) and 1 out of 4 consonants (for end) and 4 letters will be remaining

So n(A)= 2(vowels) × 4(consonants) × 4!(remaining letters arranged)

P(A)= n(A)/n(S) = 2×4×4! / 6! = 8/30 = 4/15