find the number of distinct arrangements of the letters of the word IITJEE that can be made preserving the order in which the vowels(I,I,E,E) occur and not counting the original arrangement IITJEE

let us put the vowels in order   _I_I_E_E_

The remaining two letters can be put in either of 5 spaces . So number of ways = 5x5 =25

but when the letters TJ is put in same space , we can arrange it in two ways so , there are 5 more ways

so now number of ways =25+5=30

dropping the IITJEE we have 29 ways .