Question

From the letters of the word ${}^{\prime }DAUGHTE{R}^{\prime }$, how many words can be formed each consisting of $2$ vowels and $3$ consonants?

• A. $32$
• B. $15$
• C. $30$
• D. $16$

Answer 1

The correct option is C $30$

$DAUGHTER$

$A,U,E$ are vowels

$D,G,H,T,R$ are cosonants

$2$ vowels $3$ consonants

Nmber of word

${}^3{C}_2{\times }^5{C}_{3r}$

$=3\times \frac{5\times 4}{2}=3\times 10=30$