 Hi and welcome to the session. I am Priyanka and let us discuss the following question. It says how many three-digit numbers can be formed from the digits 1, 2, 3, 4 and 5? Assuming that repetition of the digits is allowed, repetition of the digits is not allowed. Now, before proceeding on with the solution, we should be well versed with the fundamental principle counting. It says that the total number of occurrence of the event in a given order is, if an event can occur in M different ways following which another event can occur in N different ways, then the total number of occurrence of the event in the given order is M multiplied by N. This is the fundamental principle of counting which we will be using in our question. The knowledge of this is the key idea of our question. So, let us start with the solution for the first part where repetition, there are as many numbers as there are ways of filling digits in the three vacant places. We have two fill digits in the three right now in succession by the five given digits that are 1, 2, 3, 4 and 5. Now, there are as many numbers as there are ways of filling digits in the three vacant places. Let us first take the first place. Now, this first place can be filled by any one of the five digits. So, there are five different ways of filling this first place can be filled by any of the five digits since repetition of the digits is allowed. So, here also we have five different ways because repetition of the digits are allowed. And similarly, for the third place also, we have five different ways of filling up the third place. The number of ways in which these three vacant places can be filled by the multiplication principle that is the fundamental principle of counting that we learned in our key idea is 5 multiplied by 5 multiplied by 5 which gives us 125. So, the number of three digits number that can be formed by 1, 2, 3, 4 and 5 when repetition of digits is allowed is 125. Right? So, this completes our first part. Now, let us proceed on with our second part. Here, repetition of the digits are not allowed. Right? So, here also we need to fill digits in three vacant places. Here also the numbers which are given to us are 1, 2, 3, 4 and 5. So, the first place can be filled up by any of the five digits which are available. So, we have five different ways of filling this first place. Now, for the second place here, since the repetition of the digits are not allowed, there are only four different ways which are left with us because one digit we must have put in the first place. So, we are left with four digits and hence four different ways. Similarly, the third place can be filled up with now three different ways. And after applying the multiplication principle the number of ways in which these three vacant places can be filled in is 5 multiplied by 4 multiplied by 3 that is equal to 60. So, there are 60 different numbers that can be formed by using 1, 2, 3, 4, 5 and the numbers have to be a three digit number. This completes our session. I hope you enjoyed the session. Here we used the fundamental principle of counting or the multiplication principle. Bye for now.