Question

The number of arrangements that can be formed out of GANESHPURI SO that
(iii) The vowels occupy even places are:

• A. ${}^5{P}_4{.}^5{P}_5$
• B. ${}^5{P}_4{.}^6{P}_6$
• C. ${}^5{P}_4{.}^6{P}_4$
• D. ${}^5{c}_4{.}^6{P}_6$

Answer 1

Answer: (A)

${}^5{P}_4{.}^5{P}_5$

$5$ places $(2,4,6,8,10)$ for $4$ vowels$\Rightarrow {}^5{C}_4\times 4!$ & remaining $5\to 5!$

$\Rightarrow {}^5{C}_4\times 4!\times 5!$

$\Rightarrow {}^5{P}_4\times {}^5{P}_5\Rightarrow \left(A\right)$.