Question

In how many ways can a consonant and a vowel be chosen out of the letters of the word logarithm

Answer 1

no. of constants are 6 no. of vowels are 3
no. of ways to select a constant 6C1
no. of ways to select a vowel 3C1
total no. of ways 6C1×3C1

Answer 2

Answer:

Total ways can a consonant and a vowel be chosen out of the letters of the word logarithm is 18.

Step-by-step explanation:

To find : In how many ways can a consonant and a vowel be chosen out of the letters of the word logarithm?

Solution :

The word is 'LOGARITHM'

Vowels - O,A,I - 3

Consonants - L,G,R,T,H,M - 6

Ways of choosing a vowel is $^3C_1$

Ways of choosing a consonants is $^6C_1$

Total ways can a consonant and a vowel be chosen out of the letters of the word logarithm is

$n=^3C_1\times ^6C_1$

$n=\frac{3\times 2\times1}{2\times 1}\times \frac{6\times 5!}{5!}$

$n=3\times6$

$n=18$

Therefore, Total ways can a consonant and a vowel be chosen out of the letters of the word logarithm is 18.