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# Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

$\begin{array}{1 1}(A)\;60\\(B)\;120\\(C)\;7200\\(D)\;720\end{array}$

Toolbox:
• $C(n,r)=\large\frac{n!}{r!(n-r)!}$
• $n!=n(n-1)(n-2)(n-3)......(3)(2)(1)$
The no of ways of the consonants =$5C_3$
$\Rightarrow \large\frac{5!}{3!2!}$
$\Rightarrow \large\frac{5\times 4\times 3!}{3!\times 2}$
$\Rightarrow 10$
The no of ways of the vowel =$4C_2$
$\Rightarrow \large\frac{4!}{2!2!}$
$\Rightarrow \large\frac{4\times 3\times 2!}{2\times 2!}$
$\Rightarrow 6$
Total number of vowels & consonants =2+3=5
No of ways the words they appear =5!
$\Rightarrow 120$
Total no of ways =$120\times 10\times 6$
$\Rightarrow 7200$
Hence (C) is the correct answer.

+1 vote