Number of 6-digit telephone numbers, which can be constructed with digits (0,1,2,3,4,5,6,7,8,9 ), if each number starts with 35 and no digit appears more than once is

Step-by-step solution

Since each number consisting of 6 digits starts with 35,3 and 5 are fixed in the first and second places. The other four places can be filled up with remaining 8 digits in ( ^8 P ₄ ) ways (=8.7 .6 .5=1680 ) ways. Hence the required number of telephone numbers is 1680 .