Question

"how many words of 2 vowels and 3 consonants may be formed from the letters of the word "facetious"

Answer 1

Here is your answer

Hope it helps you

Answer 2

Answer:

40 words

Step-by-step explanation:

Given : Word -  "facetious"

To find : How many words of 2 vowels and 3 consonants may be formed from the letters of the word "facetious".

Solution :

Number of Vowels in the given word is (a,e,i,o,u) - 5

Vowels to be chosen is 2

Number of ways to choose vowel is $^5C_2$

Number of Consonants in the given word is (f,c,t,s) - 4

Consonants to be chosen is 3

Number of ways to choose consonants is $^4C_3$

Now,

Number of ways of selecting  2 vowels and 3 consonants is

$=^5C_2\times ^4C_3$

$=\frac{5!}{2!\times3!}\times \frac{4!}{1!\times3!}$

$=\frac{5\times 4\times3!}{2\times 1\times3!}\times \frac{4\times 3!}{1\times3!}$

$=\frac{5\times 4}{2}\times \frac{4}{1}$

$=10\times 4$

$=40$

Therefore, There are 40 ways in which word form.