The number 916238457 is an example of 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. Number of such numbers are (2024)

1

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Combination with Restrictions

The number 91...

A

2268

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C

2975

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D

1560

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Solution

The correct option is B

2520

The conditions are:

1. The digits from 1 to 5 should be in their natural order.

2. The digit 6 should be placed such that the digits 1 to 6 DO NOT occur in their natural order.

3. The other digits: 7, 8 and 9 are placed in other places.

We only have one way of doing step 1. We have 5 digits and 6 spaces like this:

_1_2_3_4_5_

In doing step 2, we can place the digit 6 in any of the first 5 spaces. Thus we have 5 ways of doing step 2.

Similarly, in doing step 3, we have 7, 8 and 9 ways of placing the digits 7, 8 and 9 respectively.

So, there are 1×5×7×8×9=2520 numbers that satisfy the given conditions.


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The number 916238457 is an example of 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. Number of such numbers are (3)

The number 916238457 is an example of 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. Number of such numbers are (4)

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The number 916238457 is an example of 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. Number of such numbers are (5)

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The number 916238457 is an example of 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. Number of such numbers are (2024)
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