 Hello friends that's all the following question it says determine n if 2nc3 is to nc2 is equal to 12 is to 1 and 2nc3 is to nc3 is equal to 11 is to 1. Let us first discuss the first part we are given that 2nc3 is to nc2 is equal to 12 is to 1 that is 2nc3 upon nc2 is equal to 12 upon 1 and this implies 2n factorial upon 3 factorial into 2n-3 factorial upon n factorial upon 2 factorial into n-2 factorial is equal to 12 upon 1 and this implies 2n factorial upon 3 factorial into 2n-3 factorial into 2 factorial into n-2 factorial upon n factorial is equal to 12. Now this again implies 2n factorial can be written as 2n into 2n-1 into 2n-2 into 2n-3 factorial upon 3 factorial can be written as 3 into 2 into 1 into 2n-3 factorial into 2 factorial into n-2 factorial upon n factorial n factorial can be written as n into n-1 into n-2 factorial and this is equal to 12. Now 2n-3 factorial gets cancelled with 2n-3 factorial n-2 factorial gets cancelled with n-2 factorial n gets cancelled with n 2 gets cancelled with 2 and we have n-1 into 2n-2 upon 3 into 2 upon n-1 is equal to 12 and this implies 2n-1 taking to common from this we have 2 into n-1 into 2 upon 3 into n-1 is equal to 12. Now n-1 gets cancelled with n-1 and we have 4 into 2n-1 upon 3 is equal to 12 and this implies 2n-1 is equal to 12 into 3 upon 4 and this implies 2n-1 is equal to 9 which again implies 2n is equal to 10 and this implies n is equal to 5. Hence n is equal to 5 for the first part of the version. Let us now discuss the second part we are given 2n-3 is to n-3 is equal to 11 is to 1. This implies 2n-3 upon n-3 is equal to 11 upon 1 this implies 2n-3 is given by 2n factorial upon 3 factorial into 2n-3 factorial upon n-3 n-3 is given by n factorial upon 3 factorial into n-3 factorial and it is equal to 11 upon 1 which again implies 2n factorial upon 3 factorial into 2n-3 factorial into 3 factorial into n-3 factorial upon n factorial is equal to 11. Now 3 factorial gets cancelled with 3 factorial now 2n factorial can be written as 2n into 2n-1 into 2n-2 into 2n-3 factorial upon 2n-3 factorial into n-3 factorial upon n factorial n factorial can be written as n into n-1 into n-2 into n-3 factorial now 2n-3 factorial gets cancelled with 2n-3 factorial n-3 factorial gets cancelled with n-3 factorial n gets cancelled with n and this whole thing is equal to 11 and this implies 2 into 2n-1 taking 2 common from here we have 2 into n-1 upon n-1 into n-2 is equal to 11. Now n-1 gets cancelled with n-1 and we have 4 into 2n-1 is equal to 11 into n-2 now we solve this for n 8n-4 is equal to 11n-22 8n-11n is equal to minus 22 plus 4 and this implies minus 3n is equal to minus 18 and this implies is equal to 18 upon 3 that is n is equal to 6 hence n is equal to 6 for the second part of the question so to the first part answer is 5 and to the second part answer is 6 so this completes the question why for now take care have a good day