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 in 6 do not. Number of such numbers are
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 in 6 do not. Number of such numbers are
The correct option is B 2520
The required conditions to be satisfied are,
i) the number must be 9 digit number containing 1 to 9
digits once
ii) digits 1 to 5 must occur in consecutive order
iii) digits 1 to 6 must not occur in consecutive order
So, condition (i) is fulfilled in only one way. So, places
of 1 to 5 are fixed in the number.
Now, we have 5 digits and 6 places (_1_2_3_4_5_)
Now, we can place 6 in any of the first 5 places. Therefore,
total number of ways to do it is 5.
Similarly, following the same to place 7, 8 and 9, we have
7, 8 and 9 places respectively.
Therefore, by multiplication rule of counting, we have
⇒1×5×7×8×9=2520 number of ways
Hence, this is the required result.
The required conditions to be satisfied are,
i) the number must be 9 digit number containing 1 to 9 digits once
ii) digits 1 to 5 must occur in consecutive order
iii) digits 1 to 6 must not occur in consecutive order
So, condition (i) is fulfilled in only one way. So, places of 1 to 5 are fixed in the number.
Now, we have 5 digits and 6 places (_1_2_3_4_5_)
Now, we can place 6 in any of the first 5 places. Therefore, total number of ways to do it is 5.
Similarly, following the same to place 7, 8 and 9, we have 7, 8 and 9 places respectively.
Therefore, by multiplication rule of counting, we have
⇒1×5×7×8×9=2520 number of ways
Hence, this is the required result.
