How many different words can be formed by using all the letters o( the word 'ALLAHABAD' such that vowels  occupy the even positions, is

There are 4 vowels and all are alike i.e. 4A's. Also, there are 4 even places viz 2nd, 4th, 6th and 8th. So, these 4 even places can be occupied by 4 vowels in 4!4!=1 way. Now, we are left with 5 places in which 5 letters, of which two are alike (2 L's) and other distinct, can be arranged in 5!2! ways.Hence, the total number of words in which vowels occupy the even places =5!2!×4!4!=5!2!=60