Question

in how many ways 4 cards can be drawn from a pack of 52 playing cards so that there is atleast one face card​(permutation and combination)

Answer 1

Answer: 179335

Step-by-step explanation:

Well, there are four conditions in this problem:

1) 1 face card and 3 non-face cards

2) 2 face cards and 2 non-face cards

3) 3 face cards and 1 non-face card

4) 4 face card and 0 non-face cards

for condition (1),

1 out of 12 face cards must be chosen, so it will be 12C1 and three non face cards which will be 40C3 ( the complete set is 40 here as we don't count 12 face cards)

so this becomes 12C1 x 40C3

=> 12 x 9880 = 118560

similarly, for condition (2), it becomes

12C2 x 40C2

=>  66 x 780 = 51480

similarly, for condition (3), it becomes

12C3 x 40C1

=> 220 x 40 = 8800

for condition 4 we take 4 face cards only so it's 12C4, i.e. 495

and now we add up all of it

118560+51480+8800+495= 179335 possible combinations (probably)

Hope this helps!