In how many ways can the 4 cards be drawn from deck of 52 cards so that there is atleast one face card ?
THIS IS A QUESTION OF PERMUTATION AND COMBINATION AND NOT PROBABILITY
I know that by using the formulae :- TOTAL COMBINATION I.e 52C4 - COMBINATION OF NON FACE CARDS I.e 40C4 Gives us the answer But can we attempt the question by making 4 conditions I.e as written in question that there must be atleast 1 face card so conditions so formed will be :-
1 face card( 12C1) AND 3 non face card (40C3)
2 face card (12C2) AND 2 non face card ( 40C2)
3 face card (12C3) AND 1 non face card (40C1)
4 face cards (12C4) and no non face card
Am I attempting question in right way ? But I am not getting the correct answer .. Please HELP ME TO GET THE ANSWER FROM THE METHOD AS SUGGESTED BY ME ABOVE IF IT IS FLAWLESS . IF IT HAS ANY FLAW PLEASE PLEASE PLEASE EXPLAIN IN DETAIL