In a city all telephone numbers have six digits. The first two digits are always 41 or 42 or 46 or 62. How many telephone numbers have all six distinct digits?

Explanation

If first two digit is 41, the remaining 4 digits can be arranged in
`= ""^(8)P_(4) = (8"!")/(8 - 4"!") = (8"!")/(4"!")`
`= (8 xx 7 xx 6 xx 5 xx 4"!")/(4"!")`
` = 8 xx 7 xx 6 xx 5 = 1680`
Similarly, if first two digit is 42, 46, 62 or 64, the remaining 4 digits can be arranged in `""^(8)P_(4)` ways i.e., 1680 ways.
`therefore` Total number of telephone numbers have all six digits distinct `= 5 xx 1680 = 8400`