 Hi and how are you all? Let's discuss this interesting question. It says how many 5 digit telephone numbers can be constructed using digits 0 to 9 if each number starts with 6, 7 and no digit appear more than once. That means we cannot repeat the digits. Let us start with our solution. Now here we can make as many telephone numbers as there are ways of filling digits in 5 vacant places. We need to fill digits in 5 vacant places. Now the first and the second place is filled up by 6 and 7 as it is given to us in the question. So the first place can only be filled up by one way. The second place can also be filled up only by one way. Proceeding on to the third place we can fill up it with remaining 8 digits as we cannot repeat the digits and hence it will be by 8 different ways. Out of 0 to 9 we have in all 10 digits. Out of that 2 digits are occupied so there are 8 ways left. The fourth place now can be filled up only by 7 ways and the last place can be filled up by 6 different ways. Thus since repetition was not allowed by the multiplication principle the number of ways of filling up these 5 vacant places will be 1 multiplied by 1 multiplied by 8 multiplied by 7 multiplied by 6 that is 3 3 6. So the number of 5 digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 6 7 and no digit appear more than once then the required answer is 3 3 6 different ways. So this completes the question. I hope now you understood the multiplication principle or the fundamental principle of counting well. Bye for now.