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Q.

How many numbers between 5000 and 10000 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?

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a

5×8P3

b

5×8C8

c

5!×8P3

d

5×8C3×3!

answer is A, D.

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Detailed Solution

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We are to form 4-digit numbers with either 5 or 6 or 7 or 8 or 9 at the thousand's place. 

4-digit number :     X    X    X    X            1     2    3 4

No. of ways of filling 1st place = 5 After filling 1st -place, we have 8 digits to be used. 

No. of ways of filling 2 nd , 3 rd, 4 th places =  8P3

Total no. of numbers formed =5×8P3

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