Permutations and Combinations
How many digit telephone numbers can be constructed using the digits to if each number starts with and no digit appears more than once?
Solution: It is given that the 5-digit telephone numbers always start with 67.
Therefore, there will be as many phone numbers as there as ways of filling 3 vacant places by the digits 0-9, keeping in mind that the digits cannot be repeated.
The unit place can be filled by any of the digits from 0-9, expect digits 6 and 7.
Therefore, the unit place can be filled in 8 different ways following which, the tens place can be filled in by any of the remaining 7 digits in 7 different ways, and the hundreds place can be filled in by any of the remaining 6 digits in 6 different ways.
Therefore, by the multiplication principle, the required number of ways in which 5- digit telephone numbers can be constructed is