Q. 265.0( 2 Votes )

How many 6-digit telephone numbers can be constructed with digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?

Answer :

Given, numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9


The total number of these digits are 10


To find: 6-digit telephone numbers starting with 35 and no digit appears more than once


So, fix the position of first two digits as 3 and 5



Now, we need to fill these 4 remaining places


Remaining number of digits are 8 (0, 1, 2, 4, 6, 7, 8, 9)


Arrange these 8 numbers at 4 places.


Formula used:


Number of arrangements of n things taken r at a time = P(n, r)



The total number of ways


= the number of arrangements of 8 things taken 4 at a time


= P(8, 4)





= 8 × 7 × 6 × 5


= 1680


Hence, possible number of 6-digit telephone numbers starting with 35 are 1680


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