The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is `576` b. `\ ^4C_3xx4!` c. `2xx4!` d. none of these

Explanation

The even places can be occupied only by consonants (RTCL)

we select `3` out of `4` to occupy these `3` places = `4_(C_3)`=4

They can themselves arrange in `3!` ways =`6` ways
total =`6.4` ways =`24` ways

For the odd places remaining `4` letters will arrange themselves in 4! ways =`24` ways

So, total =`24.24` ways =`576` ways