 Hi, and welcome to the session. Let us just ask the following question. The question says from a committee of eight persons, in how many ways can we choose a chairman and a vice-chairman assuming one person cannot hold more than one position? Before solving this question, we should first be well-posed with theorem one given in your NCRT book. The theorem one states that the number of permutations, different objects taken r at a time, objects do not repeat is the number of different objects and r is the number of objects taken at a time. And this NPR is equal to N factorial upon N minus r factorial. We will use this theorem as key idea to solve this question. Now, begin with the solution. Look at the question again. The question says from a committee of eight persons in how many ways can we choose a chairman and a vice-chairman assuming one person cannot hold more than one position? In this question, we have to find number of ways in which a chairman and a vice-chairman can be chosen when one person cannot hold more than one position. That means the same person cannot hold both the positions. Here, we have eight different persons and we have to choose two persons out of them as only one person can hold one position as no repetition is allowed. Therefore, number of ways in which a chairman vice-chairman can be chosen when person can hold only one position is equal to number of permutations of eight different persons at a time. In theorem one, we know that number of permutations of n different objects take an r at a time and the objects do not repeat is NPR. In theorem one, we know that number of permutations of n different objects take an r at a time and the objects do not repeat is NPR. The n different objects are eight different persons and r is 2 and one person can hold only one position. So this means number of permutations of eight different persons taken two at a time is 8p2. We know that np r is equal to n factorial upon n minus r factorial. Here n is 8 and r is 2 so 8p2 is equal to 8 factorial upon 8 minus 2 factorial and this is equal to 8 factorial upon 6 factorial and this is equal to 8 into 7 into 6 factorial upon 6 factorial canceling 6 factorial from both numerator and denominator we are left with 8 into 7 8 into 7 is 56 and so required answer is 56. This completes the session. Bye and take care.