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Bunuel
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The number 916238457 is an example of nine digit number which contains Thu Feb 11, 2021 6:15 am
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85% (hard)

Question Stats:

35% (02:22) correct 65% (02:01) wrong based on 51 sessions

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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

(A) 2268
(B) 2520
(C) 2975
(D) 3560
(E) 3660


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chetan2u
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GMAT Focus 1: 735 Q90 V89 DI81
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The number 916238457 is an example of nine digit number which contains Thu Feb 11, 2021 7:03 pm
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Bunuel
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

(A) 2268
(B) 2520
(C) 2975
(D) 3560
(E) 3660


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Digit 9, 8 and 7 can be placed anywhere and can take 9*8*7 combinations.
There is a restriction on digit 6 and also on 12345 being in that order.
So place 12345 in that order with gaps in between each consecutive pair.
_1_2_3_4_5_. This can be done in only one way
Next we can choose a place for 6 from first 5 gaps leaving the gap after 5, so 5 ways.

Total ways =9*8*7*1*5=2520
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