Question 1195492: How many 5-digit numbers can be formed using numbers 0, 1, 2, …9, such that the first digit must not be 9 and repetition is not allowed
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How many 5-digit numbers can be formed using numbers 0, 1, 2, …9, such that the first digit must not be 9 and repetition is not allowed
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Is a leading zero allowed, eg, 01234?
Answer by ikleyn(52814)  (Show Source):
You can put this solution on YOUR website! .
How many 5-digit  numbers can be formed using  digits 0, 1, 2, …9,
such that the first digit must not be 9 and repetition is not allowed
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Any of 8 digits {1,2,3, . . . ,8} can be in the first, most-left position
(everything except of 0 or 9), giving 8 possible options.
Any of remaining 10-1 = 9 digits can be in the next position, giving 9 possible options.
Any of remaining 9-1 = 8 digits can be in the next position, giving 8 possible options.
Any of remaining 8-1 = 7 digits can be in the next position, giving 7 possible options.
Any of remaining 7-1 = 6 digits can be in the next (= the last) position, giving 6 possible options.
The total number of 5-digit numbers satisfying the imposed conditions is 8*9*8*7*6 = 24192. ANSWER
Solved.
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To Alan:
Alan, in such problems, the leading digit 0 is PROHIBITED by default.
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