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

$\begin{array}{1 1}(A)\;3500\\(B)\;3600\\(C)\;3700\\(D)\;3800\end{array} $

1 Answer

The word DAUGHTER consists of 3 vowels and 5 consonants
2 vowels and 3 consonants may be selected in $3C_2\times 5C_3$ ways
$\Rightarrow 3C_1\times 5C_2$ ways
$\Rightarrow \large\frac{3}{1}\times \frac{5\times 4}{1\times 2}$
$\Rightarrow 30$ ways
5 letters can be arranged in 5! ways or in $5\times 4\times 3\times 2\times 1$
$\Rightarrow 120$ ways
$\therefore$ Number of words formed by 2 vowels and 3 consonants which are selected from the word DAUGHTER
$\Rightarrow 30\times 120$
$\Rightarrow 3600$
Hence (B) is the correct answer.
answered May 14, 2014 by sreemathi.v

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