Firstly select the vowels and there is only one way we can select all the vowels in ARTICLE.Now arraning A,I,E in 2nd 4rth and 6th place respectively.And total number of different way we can do that is 3!.Now remaining are RTCL.Now total number of ways in which we can arrange them is 4!.And our final aunswer is 1x3!x1x4!=144. where 1 is now of ways to select three vowels,3!is arranging the vowels.Other 1 is selecting remaining words,and 4!is arranging other remaining words.