 Hi and how are you all today? I am Priyanka. The question says determine the number of five card combination out of a deck of 52 cards if each selection of five card has exactly one king. Now let us start with our solution. We have been given a deck of 52 cards. Now here we need to find card combination. Now we have to select five cards as follow. First of all one king and this one king is out of four kings in the deck right plus four other cards and that is out of now out of 52 four has been out as kings so we are left with 48 cards. Further required number of ways for selecting one king card out of four will be four c1 right there are four c1 ways of selecting one king card similarly then four other cards out of 48 cards right so on applying the multiplication principle we have four factorial divided by one factorial multiplied by three factorial that is four minus one factorial multiplied by 48 factorial divided by four factorial 48 minus four factorial further four multiplied by three factorial divided by three factorial multiplied by 48 to 47 into 46 into 45 into 44 factorial divided by four factorial into 44 factorial further four multiplied by 48 into 47 into 46 into 45 and four factorial can be written as 4 into 3 into 2 into 1 which is which can be further simplified as we are left with 4 into 2 into 47 into 48 into 45 which is 77832 0 so the required answer was basically 4 c1 multiplied by 48 c4 so this completes the session I hope you enjoyed take care