How many arrangements of the letters of the word ‘BENGALI’ can be made if the vowels are to occupy only odd places.

There are 7 letters in the word Bengali of these 3 are vowels and 4 consonants.

There are 4 odd places and 3 even places. 3 vowels can occupy 4 odd places in $4P3$ ways and 4 constants can be arranged in  $4P4$ ways.

Number of words = $4P3$  x  $4P4$= 24 x 24 = 576