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Find the total number of 9-digit numbers...

Find the total number of 9-digit numbers which have all different digits.

Text Solution

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Number of digits are `10(0,1,2,3,4,5,6,7,8,9)`
Total number of 9-digit numbers=`.^(10)P_(9)`
out of these, the number of numbers having zero at the first place=`.^(9)P_(8)`
Hence, required number of numbers`=.^(10)P_(9)-.^(9)P_(8)`
`=10xx.^(9)P_(8)-.^(9)P_(8)=9xx.^(9)P_(8)`
`=9xx(9!)/(1!)=9xx9!`
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