No of vacancy =12
No of candidate =25
Total no of seats of SC=5
Reserved for SC=3
No of ways of filling 3 reserved vacancies by 5 scheduled caste candidates =$5C_3$
No of ways of filling rest 9 vacancies by 22 candidates =$22C_9$
$\therefore$ Required no of ways of filling vacancies =$5C_3\times 22C_9$
Hence the given statement is false.