• # question_answer How many numbers between 5000 and 10,000 can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 each digit appearing not more than once in each number [Karnataka CET 1993] A) $5{{\times }^{8}}{{P}_{3}}$ B) $5{{\times }^{8}}{{C}_{3}}$ C) $5\ !\ {{\times }^{8}}{{P}_{3}}$ D) $5\ !\ {{\times }^{8}}{{C}_{3}}$

A number between 5000 and 10,000 can have any of the digits 5, 6, 7, 8, 9 at thousand's place. So thousand's place can be filled in 5 ways. Remaining 3 places can be filled by the remaining 8 digits in $^{8}{{P}_{3}}$ ways. Hence required number =$5{{\times }^{8}}{{P}_{3}}$.