 Hello and welcome to the session. Let's discuss the following question. It says, return in the number of five card combinations out of deck of 52 cards if there is exactly one ace in each combination. To solve this question we should know the theory of combination which says our objects from n objects can be selected in NCR ways. We should also know the fundamental principle of counting which says that if event A print ways and event B is in n different ways then event A and B curve in into n ways. So this knowledge will work as key idea. Let's now move on to the solution. The total cards are 52. The number of ace is equal to 4 and cards to be selected five in numbers out of these five cards one must be ace. So the number of ways to select one ace from four ace equal to 4C1 that is 4 factorial upon 3 factorial into 1 factorial which is equal to 4. Now since we have already selected one card now we have to choose four more cards. The number of ways to select two cards from the remaining 48 cards is equal to 48C4. We have four ace then the cards different from ace are 48 in numbers and we have to select four cards from 48 cards and the number of ways is given by 48C4 which is equal to 48 factorial upon 4 factorial into 44 factorial. Now 48 factorial can be written as 48 into 47 into 46 into 45 into 44 factorial upon 4 factorial can be written as 4 into 3 into 2 into 1 into 44 factorial. Now 44 factorial gets cancelled with 44 factorial 4 into 3 into 2 is 24, 24 into 2 is 48 and this is equal to 194,580. Now the total number of ways to select three one ace equal to the number of ways to select one ace that is four into the number of ways to select four other cards this is by theory of fundamental principle of counting and this product is equal to 7,78,320 hence the answer is 7,78,320 so this completes the question bye for now take care have a good day