A) \[5{{\times }^{8}}{{P}_{3}}\]
B) \[5{{\times }^{8}}{{C}_{3}}\]
C) \[5\ !\ {{\times }^{8}}{{P}_{3}}\]
D) \[5\ !\ {{\times }^{8}}{{C}_{3}}\]
Correct Answer: A
Solution :
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 =\[5{{\times }^{8}}{{P}_{3}}\].
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