 Hello friends, let's solve the following question. It says, in how many ways can one select a cricket team of 11 from 17 players in which only 5 players can ball? If each cricket team of 11 must include exactly 4 ballers. Let us understand the key idea behind this question. R objects from N objects can be selected in NCR ways. And we should also know the fundamental principle of counting which says that event A occurs in N ways, event B occurs in N ways, then event A and B occur in M into N ways. This knowledge will work as key idea behind this question. Let us now move on to the solution. If total players are 17, number of ballers are 5 and the number of other players is equal to 17 minus 5 that is 12. Now we have to select a team of 11 players which consists of 4 ballers and 7 other players. The number of ways to select 4 ballers from 5 ballers is equal to 5 C4. This is by theory of combination. Let's discuss the key idea. Similarly, number of ways to select 7 other players is equal to 12 C7. Now the total number of ways to select 11 players in which exactly 4 are ballers is equal to the number of ways to select 4 ballers from 5 ballers that is 5 C4 into number of ways to select 7 other players from 12 other players. This is by the fundamental principle of counting as we discussed in the key idea is equal to 5 factorial upon 4 factorial into 1 factorial into 12 factorial upon 7 factorial into 5 factorial. 5 factorial gets cancelled with 5 factorial and we have 12 factorial can be written as 12 into 11 into 10 into 9 into 8 into 7 factorial upon 7 factorial into 4 factorial and 4 factorial can be written as 4 into 3 into 2 into 1. Now 7 factorial gets cancelled with 7 factorial 2 3 is 12 and it gets cancelled with 12 and now this is equal to 11 into 5 into 9 into 8 and it is equal to 3960. Hence the total number of ways to select 11 players in which there are exactly 4 ballers is 3960. Complete the question. Hope you enjoyed this session. Goodbye and take care.