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The number 916238457 is an example of a ...

The number 916238457 is an example of a nine-digit number which contains each of the digit 1 to 9 exactly once. It also has the property that the digits 1 to 5 occur in their natural order, while the digits 1 to 6 do not. Find the number of such numbers.

Text Solution

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The correct Answer is:
2520
6 places can be selected in `.^(9)C_(6)` ways and 6 can be placed only at 5 places except the right most of the 6 selected. Remaining numbers , i.e., 7,8,9 in 3! Ways.
Hence, number of numbers are `.^(9)C_(6). 5.3!=84xx30=2520`
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