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?

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 $= 5!\times 30=120\times 30=3600$

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