Question

In how many ways can the letters of the word vowels be arranged, if the letters $oe$ can only occupy odd places.

Answer 1

Given word $vowels$ can be arranged as $oe$ in odd places as follows:

1) $\left(oe\right)vwls$, this can be arranged in $4!\times 2!=48$

Similarly,

2)$vw\left(oe\right)ls$, this can be arranged in $4!\times 2!=48$

3)$vwls\left(oe\right)$, this can be arranged in $4!\times 2!=48$

So by adding up three we get $48+48+48=144$ is the required solution