Question

How many 5-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

Here the unit place can be filled by any one of the digits 0.1,2,3,4,5,8,9. So the unit place can be filled in 8 ways. Now the tens place can be filled in 7 ways by remaining 7 digits. The hundreds place can be filled in 6 ways by remaining 6 digits. Since the thousands and ten thousands place are already filled, they can be filled only in one way.

$\therefore$ Total number of 5-digit telephone number = $6\times 7\times 8=336.$