Question

How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters out of word daughter ?

Answer 1

Answer:

3600

Step-by-step explanation:

DAUGHTER This  word consist of 8 letters,out of which 3 are vowels(u,a,e) and remaining 5 (d,g,h,t,r) are consonants.

we have to form 5 letter words such that it should contain 2 vowels and 3 consonants. For that first we should select 2 vowels out of 3 vowels which can be done in 3c2 ways and 3 consonants out of 5 consonants which can be done in 5c3 ways. Now as we got 5 letters we have to arrange them.Since the any of the letters are not repeated those 5 letters can be arranged in 5! ways. So first we have to select the relevant items and then have to arrange them. Finally the required answer is 3c2*5c3*5! =3*10*120=3600

Answer 2

Here Is Your Answer Mate....;

No. of Vowels in the word – DAUGHTER is 3.

No. of Consonants in the word Daughter is 5.

No of ways to select a vowel = 3c2 = 3!/2!(3 – 2)! = 3

No. of ways to select a consonant = 5c3 = 5!/3!(5 – 3)! = 10

Now you know that the number of combinations of 3 consonants and 2 vowels = 10x 3 = 30

Total number of words = 30 x 5! = 3600 ways

Hope it's Helpful....:)