 Hello and welcome to the session. Let's discuss the following question. It says, A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected. To solve this question, we should know the theory of combination which says, R objects from N objects can be selected in CR ways. And we should also know the fundamental principle of counting which says, if event A occurs in and event B occurs in, then event A and B occur in M into N ways. This knowledge is the key idea. Let's now move on to the solution. We have to select 2 black and 3 red balls from 5 black and 6 red balls. So the number of ways to select 2 black balls from 5 black balls is equal to 5 C2. And the number of ways to select 3 red balls, 6 red balls. The total number of ways 2 black red balls is equal to 5 C2 into 6 C3. This is the fundamental principle of counting. Discuss in the key idea. And it is equal to 5 factorial upon 2 factorial into 5 minus 2 factorial that is 3 factorial into 6 factorial upon 3 factorial into 3 factorial. Again equal to 5 factorial can be written as 5 into 4 into 3 factorial upon 2 factorial into 3 factorial into 6 factorial can be written as 6 into 5 into 4 into 3 factorial upon 3 factorial can be written as 3 into 2 into 1 into 3 factorial factorial gets cancelled with 3 factorial 2 into 2 is 4 and this is equal to 200. Hence the total number of ways to select 2 black and 3 red balls is 200. And this is the required answer. So this completes the question. Hope you enjoyed the session. Goodbye and take care.