How many 6-digit telephone numbers can be constructed using the digits 0 to 9, if each number starts with 67 and no digit appears more than once?

To find: 6-digit telephone numbers that can be constructed using the digits 0 to 9.


Condition: each number starts with 67 and no digit appears more than once



There are 10 digits between 0 to 9,and two of them are utilized in filling up the first two digits i.e.67 of the 6 digit phone number, so remaining number of digits=10-2=8,and this need to be used in filling up the remaining 6-2=4 places of the telephone number.


So, number of ways=8 × 7 × 6 × 5=1680.


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