 Hi, I'm Kanika and I'm going to help you to solve the following question. The question says, find R, F first part is 5 PR is equal to 2 into 6 PR 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. In this question, we have to find R if 5 PR is equal to 2 into 6 PR minus 1. We know that NPR is equal to N factorial upon N minus R factorial therefore 5 PR is equal to 5 factorial upon 5 minus R factorial and 6 PR 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 minus R plus 1 factorial is equal to 6 minus R plus 1 into 6 minus R into 6 minus R minus 1 factorial and 6 factorial is equal to 6 into 5 factorial. Now we will substitute 6 minus R plus 1 into 6 minus R into 6 minus R minus 1 factorial in place of 6 minus R plus 1 factorial and 6 into 5 factorial in place of 6 factorial. So by substituting we get 5 factorial upon 5 minus R factorial is equal to 2 into 6 into 5 factorial upon 6 minus R plus 1 into 6 minus R into 6 minus R minus 1 factorial. Now this implies 5 factorial upon 5 minus R factorial is equal to 2 into 6 into 5 factorial upon 7 minus R into 6 minus R into 5 minus R factorial. Now 5 factorial cancels out from both sides and 5 minus R factorial also gets cancels out from both the sides. So now we are left with 1 is equal to 12 upon 7 minus R into 6 minus R and this implies 7 minus R into 6 minus R is equal to 12 and this implies 42 minus 13 R plus R square is equal to 12 and this implies R square minus 13 R plus 30 is equal to 0 and this implies R minus 10 into R minus 3 is equal to 0 and this implies R is equal to 10 or R is equal to 3. We have to find value of R in the expression 5 factorial upon 5 minus R factorial is equal to 2 into 6 factorial upon 6 minus R plus 1 factorial. If we put R as 10 in this expression then we will get 5 factorial upon minus 5 factorial which is not a possible situation as factorial of negative numbers is not possible. So this implies that the value of R is 3 hence a required answer is R is equal to 3. This completes the session. Bye and take care.