Q.1.    How many words, with or without meaning, each of 2 vowels and 3 consonants

           can be formed from the letters of the word DAUGHTER?
          

Answers (1)
S seema garhwal

In the word DAUGHTER, we have 

vowels = 3(A,E,U)

consonants = 5(D,G,H,T,R)

Number of ways of selecting 2 vowels =^3C_2

Number of ways of selecting 3 consonants =^5C_3

Therefore, the number of ways of selecting 2 vowels and 3 consonants =^3C_2 .^5C_3

                                                                                                           =3\times 10=30

Each of these 30 combinations of 2 vowels and 3 consonants can be arranged in 5! ways.

Thus, the required number of different words = 5!\times 30=120\times 30=3600

 

 

 

Exams
Articles
Questions