Question

Let n be the number of ways in which the letters of the word "RESONANCE" can be arranged so the vowels appear at the even places and m be the number of ways in which "RESONANCE" can arrange so that letters R,S,O,A appears in the order same as the word RESONANCE, then answers the following questions.
The value of n is

• A. 360
• B. 720
• C. 240
• D. 840

Answer 1

The correct option is B 720

RESONANCE

VOWELS $=E,O,A,E$

CONSTANTS $=k,S,N,N,C$

$\overline{1}\overline{\left(2\right)}\overline{3}\overline{\left(4\right)}\overline{5}\overline{\left(6\right)}\overline{7}\overline{\left(8\right)}\overline{9}$

$\Rightarrow$ vowels can be arranged as $=\frac{4!}{2!}$

$\Rightarrow$ consonants can be as $=\frac{5!}{2!}$

Total No. of ways

$\frac{4!}{2!}\times \frac{5!}{2!}=\frac{24}{2}\times \frac{120}{2}=12\times 60=720$