Question:
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all si x digits distinct?
Solution:
According to the question,
All telephone numbers have six digits
Given that,
The first two digits = 41 or 42 or 46 or 62 or 64
Hence, the number of 2 digits that the telephone number begins with =5
First two digits can be filled in 5 ways,
The remaining four-digits can be filled in 8P4 ways,
8P4 = 8!/(8 – 4)! = 1680
Therefore, number of telephone numbers having six distinct digits =5×1680
=8400