How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
720
360
1420
1680
Explanation:
The first two places can only be filled by 3 and 5 respectively and there is only 1 way for doing this.
Given that no digit appears more than once. Hence we have 8 digits remaining (0,1,2,4,6,7,8,9)
So, the next 4 places can be filled with the remaining 8 digits in 8P4 ways.
Total number of ways = 8P4=8×7×6×5=1680