 Hi, and welcome to the session. Let us discuss the following question that question says, find r if second part is 5pr is equal to 6pr minus 1. Before solving this question, we should know that npr is equal to n factorial upon n minus r factorial. The knowledge of this formula is the key idea in this question. Let's now begin with the solution. We have to find r if 5pr is equal to 6pr minus 1. We know that npr is equal to n factorial upon n minus r factorial. So by using this formula, 5pr is equal to 5 factorial upon 5 minus r factorial. And 6pr minus 1 is equal to 6 factorial upon 6 minus r plus 1 factorial. As n factorial is equal to n into n minus 1 factorial, therefore, 6 factorial is equal to 6 into 5 factorial. And 6 minus r plus 1 factorial is equal to 6 minus r plus 1 into 6 minus r into 6 minus r minus 1 factorial. Now we will substitute 6 into 5 factorial in place of 6 factorial and 6 minus r plus 1 into 6 minus r minus 1 factorial in place of 6 minus r plus 1 factorial. By substituting these values, we get 5 factorial upon 5 minus r factorial is equal to 6 into 5 factorial upon 7 minus r into 6 minus r into 5 minus r factorial. Now 5 factorial and 5 minus r factorial cancels out from both sides. So we are now left with 1 is equal to 6 into 1 upon 7 minus r into 6 minus r. And this implies 7 minus r into 6 minus r is equal to 6. And this implies 42 minus 13 r plus r square is equal to 6. And this implies r square minus 13 r plus 36 is equal to 0. And this implies r square minus 9 r minus 4 r plus 36 is equal to 0. And this implies r minus 9 into r minus 4 is equal to 0. And this implies r is equal to 9 or r is equal to 4. We have to find the value of r in the expression 5 factorial upon 5 minus r factorial is equal to 6 factorial upon 6 minus r plus 1 factorial. If we put r as 9 in this expression, then we will get factorial of negative number, which is not possible. So 9 is not a value of r. That means r is equal to 4 is our required answer. Hence the required value of r is 4. This completes the session. Bye and take care.