Question

How many five digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?

Answer 1

The first two digits are fixed as 67.
As repetition of digits in not allowed, the number of available digits to fill the remaining places is 8.
The third place can be filled in 8 ways.
The fourth place can be filled in 7 ways.
The fifth place can be filled in 6 ways.
Total number of such telephone numbers = 8$\times$7$\times$6 = 336