 Hello and welcome to the session. Let's discuss the following question. It says, in how many ways can a student choose a program of five courses if nine courses are available and two specific courses are compulsory for every student? To solve this question we need to know the theory of combination which says our objects from n objects can be selected in n-c-r ways and we also need to know the fundamental principle of counting which says if event A occurs in m different ways and event B occurs in different ways then event A and B occur in m into n ways. This knowledge will work as key idea. Let us now move on to the solution. The total courses are nine and courses to be selected, seven numbers and number of compulsory courses is equal to two. Now the number of remaining non compulsory courses is equal to nine minus two that is seven and number of non compulsory courses selected is equal to i minus two that is three. Now we have to select five courses out of which two are compulsory and three are non compulsory. So the number of ways to select two compulsory courses from two compulsory courses is equal to two C2 and the number of ways to select non compulsory courses from seven non compulsory courses is equal to seven C3. This is the theory of combination discussed in the key idea. Now the total number of ways to select five courses is equal to the number of ways to select two compulsory courses that is two C2 into the number of ways to select three non compulsory courses and this is equal to two factorial upon two factorial into zero factorial into seven factorial upon three factorial into four factorial and it is equal to one into seven factorial can be written as seven into six into five into four factorial three factorial can be written as three into two into one into four factorial four factorial gets cancelled with four factorial three into two is six six gets cancelled with six and we have seven into five and it is equal to thirty five and the total number of ways to select five courses is thirty five and this is the required answer. So this completes the question. Bye for now. Take care. Have a good day.